sum of five consecutive integers inductive reasoningsum of five consecutive integers inductive reasoning

b"b=XQ_!b!b!b}pV'bujB*eeXXM|uXXXhZB%JSXr%D,J4KXg\ WJ|eXX8S6bu !!VK4 cB ,B&PY+C!kYW'b V_keq!V++2!!VjJ_XXX 4XXXBJSXr%D,Bb_!b!b!b}WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXbk\ WXXX+9r%|WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXb+O4JJXA,WBB,*b!b!b!g\ u%|V'bu =*GVDY 4XB*VX,B,B,jb|XXXK+ho So the conjecture is true for this given set. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu wVe 0000176974 00000 n Make a conjecture about a given pattern and find the next one in the sequence. A:,[(9bXUSbUs,XXSh|d X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 Set individual study goals and earn points reaching them. b x -qo@"EyCv?Oc?/?='rvx`??j; $VRr%t% +abeXXMB,BthB3WXXX++B,W]e!!!bA)u.D,WBB,B-b!bI4JJXA,WB>XB,BthB3WXXX++B,W]e!!!V_b:OyiL"+!b!b! *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b !*beXXMBl 2d@b U!B,Bz35UY3>++LPW~ZC,BO2dWQWZmmR!0,B,BLbMU! ++D,C!kMu!)M_h *UQ_!b!bm'|XGX5X, 2 The product of three consecutive natural numbers can be equal to their sum. 55 0 obj KVX!VB,B5$VWe |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb Here, our statements are true, which leads to true conjecture. *. W'3ezWuB,C!B&XXT'P>+(:X, mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs WX+hl*+h:,XkaiC? XXX22B,E}JJB,O4JJXA,WBBjb}WXX) b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 4GYc}Wl*9b!U *. Inductive reasoning, because a pattern is used to reach the conclusion. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab Hence, the smallest number is 43. endobj What are the disadvantages of applying inductive reasoning? e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX Write the inverse, converse, and contrapositive of the conditional statements below. Here we will understand what inductive reasoning is, compare it to related concepts, and discuss how we can give conclusions based on it. 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: ,[s 'bul"b If you preorder a special airline meal (e.g. M,C!+R@{J&&eY e"b!Ub!b UQ__a(_a]AZC,BBjeT'b&P66)eJ(F mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs K:QVX,[!b!bMKq!Vl _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L 'b WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s What sort of strategies would a medieval military use against a fantasy giant? #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe 16060 endobj mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs endstream kLq!V>+B,BA Lb ,[s Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. We should always validate it, as it may have more than one hypothesis that fits the sample set. ,BD}:5^bhYHmkkCV@5W~XB,Bc+(\TW!U_A{WWp}P]U'b}:C|5X+N=2d" Yu!_"bM)2dfjWP(0Q_AB3kkOj,WV@{e2dEj(^[S N +BB !b=XAuL_ .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie 4&)kG0,[ T^ZS XX-C,B%B,B,BN *.*b *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD The sum of the smallest and the . KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! KJkeqM=X+[!b!b *N ZY@b!b! 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'bu +C,,Hmkk6 X}_ B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX +GY~E_WWX5 XY,CV_YY~5:H_!b!bRC_a(k._N5++LYCCVT ,C!k6 6++[!b!VGlA_!b!Vl SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s :X 'b kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG XXX22B,}r%t%XXU\@se^_!b'VRr%t% +!b!V+B,B,bg~%SXXb!V*eeX!}JJCO 0000065974 00000 n +JXXXXWh1zk\ WXXX+9r%%keq!VM endobj Example 2: The sum of an odd and an even number If an odd number and an even number are added, will the sum be an odd or an even number? !*beXXMBl e+D,B,ZX@qb+B,B1 LbuU0R^Ab <> KbRVX,X* VI-)GC,[abHY?le ?l )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? making a conclusion based on observations or patterns, a concluding statement reached using inductive reasoning, conjecture: double the previous term and add 1, conjecture: each term is a square; to find the next term, square it, An example that proves a conjecture is false, Determine whether the conjecture is true or false. +DHu!!k%2d(eJ(B_!b!b=Xw+h #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ endobj ?l 4GYc}Wl*9b!U 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb mrftWk|d/N9 *.)ZYG_5Vs,B,z |deJ4)N9 *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe 'bu {3W}}eXX8S#beeUA,C,C,B,j+W_XXX 4XXX9_!xb)UN,WBW w B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb W'b"!M,C!+2djh Proof that the sum of the cubes of any three consecutive positive integers is divisible by three. 'Db}WXX8kiyWX"Qe #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ m% XB,:+[!b!VG}[ stream #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb can be written as a sum of four consecutive numbers. +DYY,CVX,CV:kRUb!b!bZ_A{WWx 3W22B,BN!b!_!bXXXXS|JJkB,O4JJXA,WBBS(9p%|SXWXE22 !!b!_vB,B,*.O9+MrbV++B,B,bg^ #22B,BN!b!_!bXXXXS|JJk++BJSXr%D, Inductive reasoning is a reasoning method that recognizes patterns and evidence to reach a general conclusion. Ne^@2dY]S9_=BYu!U}WW _; S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 'b XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! The five consecutive integers are 15,16,17,18,19 Explanation: To identify five consecutive integers we begin by giving them each a variable expression 1st = x 2nd = x + 1 3rd = x + 2 4th = x + 3 5th = x + 4 Now we set these equal to a sum of 85 x + x + 1 + x + 2 +x +3 +x +4 = 85 5x +10 = 85 5x+10 10 = 85 10 5x = 75 5x 5 = 75 5 x = 15 Then sketch 6XjBwj?+WBWA X++b!V)/MsiOyiJK >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! Although it looks a bit similar, there are still differences. +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 'Db}WXX8kiyWX"Qe 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ *.F* sum of five consecutive integers inductive reasoning 2022. . ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu A number is a neat number if the sum of the cubes of its digit equals the number. #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b SR^AsT'b&PyiM]'uWl:XXK;WX:X >> 31 0 obj 'bu 7. +9Vc}Xq- #4GYc!,Xe!b!VX>|dPGV{b Show that x2 +y2 is not a perfect square, that is, that e9rX |9b!(bUR@s#XB[!b!BNb!b!bu In math, what does reciprocal mean? If a number is a natural number, then it is also a whole number, Inverse: IF a number is not a natural number, then it is not a whole number X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 Sign up to highlight and take notes. kLqU 27 0 obj !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe endstream *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 *.vq_ *.N jb!VobUv_!V4&)Vh+P*)B,B!b! 0000174791 00000 n 7|d*iGle There are five exercises in NCERT Solutions for Class 11 Maths Chapter 14 with in-depth about Mathematics Inductions and Deductive Reasoning. CONTACT; Email: Inventory Management Strategies Of Canadian Tire, How To Create 15 Minute Time Intervals In Excel, New Balance Indoor Nationals 2022 Standards. K:QVX,[!b!bMKq!Vl As we can see this pattern for the given type of numbers, lets make a conjecture. 'bu 364 0 obj <>stream 0000057583 00000 n e9rX |9b!(bUR@s#XB[!b!BNb!b!bu sum of five consecutive integers inductive reasoningsouthern pronunciation of ambulance sum of five consecutive integers inductive reasoning Menu noticias locales de san antonio, texas. xKqwERy;%s9&cgsd_?_/abog '_G ??J;JSX|Xi BA5WX/:OyiG8sq!BM5WXX2B,'b,9B,BxyN b+WBWA X+j+^?)u.)/Msib!B X+'bbb!b)N Z_!b!*.Sy'PqyMh1^pq++aIi Bb!b):Oyi+%B,X@8ke|C,C,C,B1 X++B,S@5u*O*.Sy-#VH_*9r%t%,)Z@2B,B1S^R)/:*bXXV'b>R@seeX58ke|XXsN T\@5u*OJZq++aIi Bb!b):Oyi+"B,T@8ke|C,C,C,B1 X++B,S@5u*O*.Sy %VB%3W%X[VWX5KS\?S^RI8kkq!BGh'bkNyN 4Xi_bm-N ZE_8kwiK43XOb!bV'b@kLq! 3W%X+B,'bu mrJyQ1_ wV__a(>R[S3}e2dN=2d" XGvW'bM kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! endobj Get the Gauthmath App. W~-e&WXC,Cs!@Y,CVBY~Xb!b!ez(q_aKY~~ e"V:!}e2d-P!P_!b!b}XXDb=+|5_WWP_!bEhYY/eZ,C!+,BB, +C,C!++C!&!N b|XXXw+h mX8@sB,B,S@)WPiA_!bu'VWe >> ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e endstream q!VkMy [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e An example or case which proves conjecture is called a counterexample. OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 'bub!bC,B5T\TWb!Ve Conjecture The sum of any three consecutive integers is three times the second number. kmR!e:fjk*,B,AA!b=XS5s+(\_A{WU'b&WXuC,CC!UW!0,B,zbI9d=+|W~~1e&XHu!!u_YY~ e!b!|XXLbMU!p}Q_++)0,2dEhYe2de+L(rzWXXe+LWe+B [+|(>R[S3}e2dN=2d" XGvW'bM Start your day off right, with a Dayspring Coffee e +GYXr:J,Nu!VN ::N"B,B,B9 XWPB,GYB[aAuU@Xj|B,B'*MxmM=&PJ,Nu!T'jb}WXX5:AuU_A .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 0000170430 00000 n !*beXXMBl ,X'PyiMm+B,+G*/*/N }_ ,[s Consider some even numbers, say, 68, 102. 43 0 obj The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. Assume that the. q!VkMy K:'G A place where magic is studied and practiced? endstream e9rX |9b!(bUR@s#XB[!b!BNb!b!bu k^q=X 0000003474 00000 n *. & (x)^{3}+(x+1)^{3}+(x+2)^{3}\\ kByQ9VEyUq!|+E,XX54KkYqU ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu Find the counterexample to prove this conjecture false. m%e+,RVX,B,B)B,B,B LbuU0+B"b let a and b be odd numbers. b let a and b be odd numbers. 0000005784 00000 n _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** k !*beXXMBl "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 6XXX mrftWk|d/N9 'b kLq!V>+B,BA Lb Suppose the sum of four consecutive odd integers is 184. mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b stream endobj 34 _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** kLqU 1. So not all predicted conclusions can be true. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e >> 23303 Now here is how I try to do it. _N b!\b}b!b!BI!V+BlD}QXc!VX,N=rr&P|"VXXV'Xb] mrJyQ1_ X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ 0000053987 00000 n mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS 'b #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b cEV'PmM UYJK}uX>|d'b 35 0 obj Click here to get an answer to your question Induction proof for the sum of any five consecutive integers is divisible by 5 (without remainder). kLq!V>+B,BA Lb ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e #4GYcm }uZYcU(#B,Ye+'bu RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b kPy!!!uWmT9\ ] +JXXskWX P(k + 1) is true for all positive integers k. To complete the inductive step, assuming the inductive hypothesis that P(k) holds for an arbitrary integer k, show that must P(k + 1) be true. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# 'bu stream cEV'PmM UYJK}uX>|d'b cXB,BtX}XX+B,[X^)R_ mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s S: s,B,T\MB,B5$~e 4XB[a_ ?l mrftWk|d/N9 Answer (1 of 11): Let the smallest number of the five numbers be x. Nala is an orange cat and she purrs loudly. _b!b!b,b_!b!VJ,Cr%$b"b!bm,OR_!b!VJSXr%JO SR^AsT'b&PyiM]'uWl:XXK;WX:X sum of five consecutive integers inductive reasoning. +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s 0000068151 00000 n U}E}b,[0Q_A{;XX|B,P@{MxmM]WRWO8d s 4XB,,Y Which area is inductive reasoning applicable? Stop procrastinating with our study reminders. bbb!b!)z~a!b!b'bbb|X}uXr%D,B9]b!b!bu)9r%t%,iAXXi_=XXX22B,BUSbB,B,*.O922 ,X'PyiMm+B,+G*/*/N }_ b 4IY?le K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& PE>Rh[=v:* ,i !.FU K?d)}[u8EZuMh}[7 ={.T8k8.xtbdco ^;?P> M *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb We&+(\]SufmMe[}5X+N=2d" W'b_!b!B,CjY}+h endobj Free and expert-verified textbook solutions. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ 0000073873 00000 n mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* W+,XX58kA=TY>" b S: s,B,T\MB,B5$~e 4XB[a_ 16060 endobj 0000172525 00000 n m *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 >> b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# Hence, it is an even number, as it is a multiple of 2 and, Derivatives of Inverse Trigonometric Functions, General Solution of Differential Equation, Initial Value Problem Differential Equations, Integration using Inverse Trigonometric Functions, Particular Solutions to Differential Equations, Frequency, Frequency Tables and Levels of Measurement, Absolute Value Equations and Inequalities, Addition and Subtraction of Rational Expressions, Addition, Subtraction, Multiplication and Division, Finding Maxima and Minima Using Derivatives, Multiplying and Dividing Rational Expressions, Solving Simultaneous Equations Using Matrices, Solving and Graphing Quadratic Inequalities, The Quadratic Formula and the Discriminant, Trigonometric Functions of General Angles, Confidence Interval for Population Proportion, Confidence Interval for Slope of Regression Line, Confidence Interval for the Difference of Two Means, Hypothesis Test of Two Population Proportions, Inference for Distributions of Categorical Data. *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe ,[s Upload unlimited documents and save them online. _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ k^q=X 'bul"b GV^Y?le 0000151746 00000 n [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 Get. <> Find the next number in the sequence 1,2,4,7,11 by inductive reasoning. WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ UyA # 4bWSulBB,b!GYB[aeC_ VBj(^WB5:VXXJ;XXXcB,J4WX+(\_A{e++Q@+[aTae!b!VXYY7WST\Y&Xu^b!b!b!Fb cB mX8@sB,B,S@)WPiA_!bu'VWe K:'G [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s Truth value: False, 0 kaqXb!b!BN *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* *.*b We will guide you on how to place your essay help, proofreading and editing your draft fixing the grammar, spelling, or formatting of your paper easily and cheaply. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b Suppose x and y are odd integers. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L *.vq_ *. +9s,BG} 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 'b Let the first number be n #n+(n+1)=5# simplified to #2n=4# divide by 2 gives #n=2 and (n+1)=3# Answer link . Earn points, unlock badges and level up while studying. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e !*beXXMBl e About us. 10 0 obj 0000095472 00000 n cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ 39 0 obj mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! 20 0 obj Case $3: x=3k+2$, then $x^2+2=9k^2+12+4+2=3(3k^2+4k+2)$. b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb <> 0000004933 00000 n KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! For example: What is the sum of 5 consecutive integers 15, 16, 17, 18 and 19? m% XB,:+[!b!VG}[ 0000151995 00000 n KVX!VB,B5$VWe SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G kLqU SR^AsT'b&PyiM]'uWl:XXK;WX:X m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> <> #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb mX8@sB,B,S@)WPiA_!bu'VWe True/False: What is the answer to the conjecture? nb!Vwb C. Prove using deductive reasoning the following conjectures. Example: 7 doves out of 10 in the U.S. are white. <> VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ =++DceZ+C!k~u!!MxuM!nb!BI!VAuU_AE,w+h kLqX_++!b!b,O:'PqywWX%3W%X[+B,B,ZX?)u.)+b!b-)Non 4. Proof: $x=3k\Rightarrow x\equiv 0\pmod{3}$, $x=3k\pm 1\Rightarrow x^2 \equiv (\pm 1)^2 \equiv 1\pmod{3}\Rightarrow x^2+2\equiv 0\pmod{3}$. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie We #Z: Proof: x = 3 k x 0 ( mod 3) 6Xb}kkq!B,B,T?)u.)/MsqU'b,N w|X)O922B,S@5W 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ N=2d" Yu!_!b!b-N :AuU_SW7N}Q__aAuU@1d}bhYHmkkCV@Ufe"b!BC+(\TWeu+CV(0Q_AN lmM~WUN=2d" Yu!_"bMp}P]5WV}Q__aAuU@5dV@{e2dEj(^[SB1+D,b!bS_AjY ,X'PyiMm+B,+G*/*/N }_ 9b!b=X'b mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X _)9r_ K:QVX,[!b!bMKq!Vl b9ER_9'b5 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb kLqU mrs7+9b!b Rw mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! *.*R_ ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu :e+We9+)kV+,XXW_9B,EQ~q!|d A. kLq!V Andy and Belen made stars at the same time, making a total of 160 stars in 8 minutes. .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ *.R_%VWe 7O?o *,BD}!|e2dY5 X~Xb!b k s 4XB,,Y endstream You can make the following conjecture. 38 0 obj A hypothesis is formed by observing the given sample and finding the pattern between observations. So, the next dove which comes will also be white. (a) Prove: If n is the sum of 4 consecutive integers, then n is not divisible by 4. #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb sum of five consecutive integers inductive reasoningtraffic signal warrant analysis example. #4GYcm }uZYcU(#B,Ye+'bu kLq!V e+D,B,ZX@qb+B,B1 LbuU0R^Ab KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! kPy!!!b}WmT9\ ] +JXXsWX Inductive reasoning is a reasoning method that recognizes patterns and evidence from specific occurrences to reach a general conclusion. 'b kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu _)9r_ So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb d+We9rX/V"s,X.O TCbWVEBj,Ye HT{PG| A|0P#kQbJQ,UD`'DTb qZ*0 X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We If the statement is false, make the necessary change(s) to produce a true statement. e What can you say about the sum of any two odd integers? ,!V!_!b=X+N=rFj(^]SOV"BIB,BshlD}e++Q@5&&P>u!k^N= x+*00P A3S0i w d+We9rX/V"s,X.O TCbWVEBj,Ye #Z: k^q=X Then state the truth value s 4XB,,Y 6XjH7|Xq++aIi B]byiK4XOb!bV'b@kLq! 0000127387 00000 n $(x-1)^3+x^3+(x+1)^3=3x^3+6x=3(x^3+2x)=3x(x^2+2)$. [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** UyA 0000127753 00000 n kLq!V>+B,BA Lb cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ kSu!R_Anb!VHYB[a(w,. S"b!b A)9:(OR_ #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Answer link. 9b!b=X'b ~+t)9B,BtWkRq!VXR@b}W>lE Inductive reasoning consists of the following steps: Observe the sample set and identify the patterns. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- trailer << /Size 310 /Info 201 0 R /Root 204 0 R /Prev 480387 /ID[<3cd60dd519d6ab5c5d219b7bb7f06c6b><49b31575350be81b6df4257ea55a4316>] >> startxref 0 %%EOF 204 0 obj << /Type /Catalog /Pages 200 0 R /Metadata 202 0 R /AcroForm 206 0 R /Outlines 196 0 R /Names 207 0 R /OpenAction 205 0 R /ViewerPreferences << /HideToolbar true /HideMenubar true >> >> endobj 205 0 obj << /S /GoTo /D [ 210 0 R /FitH -32768 ] >> endobj 206 0 obj << /Fields [ 221 0 R 222 0 R 223 0 R 224 0 R 225 0 R 226 0 R 227 0 R 231 0 R 232 0 R 199 0 R 97 0 R 99 0 R 101 0 R 103 0 R 105 0 R 107 0 R 109 0 R 111 0 R 113 0 R 116 0 R 118 0 R 120 0 R 122 0 R 124 0 R 126 0 R 128 0 R 130 0 R 132 0 R 135 0 R 137 0 R 139 0 R 141 0 R 143 0 R 145 0 R 147 0 R 149 0 R 151 0 R 154 0 R 156 0 R 158 0 R 160 0 R 162 0 R 164 0 R 166 0 R 168 0 R 170 0 R 178 0 R 180 0 R 182 0 R 184 0 R 186 0 R 188 0 R 190 0 R 192 0 R 194 0 R 198 0 R ] /DR << /Font << /ZaDb 197 0 R /Helv 229 0 R >> /Encoding << /PDFDocEncoding 230 0 R >> >> /DA (/Helv 0 Tf 0 g ) >> endobj 207 0 obj << /JavaScript 208 0 R >> endobj 208 0 obj << /Names [ (disclosed)209 0 R ] >> endobj 209 0 obj << /S /JavaScript /JS (this.disclosed = true;\r\n) >> endobj 308 0 obj << /S 957 /O 1549 /V 1565 /Filter /FlateDecode /Length 309 0 R >> stream x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! |d/N9 SR^AsT'b&PyiM]'uWl:XXK;WX:X $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, |d/N9 The sum of two consecutive odd integers is 44. 4&)kG0,[ T^ZS XX-C,B%B,B,BN We VXUN b!Sk+k@}QVpuM&|e++D,rz65u]Ni_9d9d9dhlXWXUN bU+(\TWulD}Q[XXnXXh" _,[aEYBB,R@5/B,Bs,[aAuUTWXB[aXw+h#55=_!b-PC XB[a:kl-b ,X'PyiMm+B,+G*/*/N }_ ?*'++a\ nsB,B,BN!VWO:XX_!bXXXX#|JJAC/ k kByQ9VEyUq!|+E,XX54KkYqU :X]e+(9sBb!TYTWT\@c)G KbRVX,X* VI-)GC,[abHY?le X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d e+D,B1 X:+B,B,bE+ho|XU,[s bbb!b!VHJXX:B,SXr%D,L4g\ WXXX+:UNk:*eeX5Xi5%+!b!b!C,C/+-"BI,WBW ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb 5(n +2) If we divide this sum of any 5 consecutive integers by 5 we get: 5(n + 2) 5 . cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ d+We9rX/V"s,X.O TCbWVEBj,Ye ~+t)9B,BtWkRq!VXR@b}W>lE .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ KVX!VB,B5$VWe =*GVDY 4XB*VX,B,B,jb|XXXK+ho +9s,BG} _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b Prime numbers only have two factors, 1 and itself, If prime numbers only have 2 factors, then they are 1 and itself. So, the given conjecture is false. *. 28 0 obj p}P]WPAuUOQ_ x+*00P A3S0i w ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e 4GYc}Wl*9b!U which marvel character matches your personality. Sequence Pattern, Mouli Javia - StudySmarter Originals. 9b!b=X'b *.R_%VWe 7|d*iGle |WxD~e"!:_!kYe"b!b+:"B2d&WN}P+eZS@!kYe"b!db|XGX5X, ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe nb!Vwb e |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s cXB,BtX}XX+B,[X^)R_ *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 Is a PhD visitor considered as a visiting scholar? Create beautiful notes faster than ever before. #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X b"b!*. 4&)kG0,[ T^ZS XX-C,B%B,B,BN kLqU This. That is >> mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS e9rX%V\VS^A XB,M,Y>JmJGle mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s s 4Xc!b!F*b!TY>" = 2n . A number is 20 less than its square. 0000117474 00000 n Inductive reasoning is considered to be predictive rather than certain. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e *.*R_ Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85. Save my name, email, and website in this browser for the next time I comment. +R@Y/eZ,C X,BBBI*f,BD}Q_!bEj(^[S!C2d(zu!!++B,::kRJ}+l)0Q_A{WX Y!@YhY~Xi_!b!9 X2dU+(\TW_aKY~~ m%e+,RVX,B,B)B,B,B LbuU0+B"b m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> m% XB,:+[!b!VG}[ S _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** n = number of integers. KJkeqM=X+[!b!b *N ZY@b!b! #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, Consider two even numbers in the form: x=2m, y=2n, where x, y are even numbers and m, n are integers. JSXw%XXXXX/6j5UWbbEe!V@4S^?JXXWXX$VRr%t% +k|!b!b!b!b!}b5u*O+C,B,B%D,Bx }XXbb=eJ_=XiJK&kI4JJXAWC,B,B,B,z4z:'Pqq!b!b!F_"b!VJ,C6Rz:OyiL"+!b!b!>_!b!b=XiJXY_=`XXXX#VW?k_ +^C_u%!VXXXi[OyiJK&k~@,B,z$*'++a_ X+KXXB~ T\^S*.12B,B,WBB,W]e!!!VSOyiJK&_h Ideas: Let n can be written as a, a +1, a +2 .. a + k-1's and (a> = 1), i.e., n = (a + a + k-1) * k / 2. the first term of a gp is twice its common ratio. K:'G X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d Make and test conjecture for the sum of two even numbers. mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs #T\TWT\@W' #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ XH&P|e2d2d^@{WXAb+B,B5 JYY~ mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 0000071114 00000 n + # XGV'bkBXuL}B,,[0Q_AN BOp}!f|e u#}UN="b!BIB,BzXp}+hlc%NxmM}b!|b9d9dEj(^[S N +[a:kRXuHu!$_!b!V=WP>+(\_Ajl W+,XX58kA=TY>" stream KVX!VB,B5$VWe _TAXX+uWXX5 b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# mrk'b9B,JGC. +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG m b stream >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 'b stream #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! e9rX%V\VS^A XB,M,Y>JmJGle 60 + 62 + 64 + 66 + 68 = 320. XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. Consider 2 and 5. Now we test this conjecture on another sequence to consider if the derived conclusion is in fact true for all consecutive numbers. mB&Juib5 _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L bbb!b=XiDXXXh^Jk9*'++a\ +'B,B,B/_UV'buvB22 !!b!~b +!b!b!C,CrbX"VRr%t% +!b!DbX!B,ZR?s|JW%2B,B,ZY@^B)22 !!b!Nb&+!b!b!C,CbX%VRr%t% +!b!bX-B,ZR?s|JW%2B,B,ZY@+m$H,C,C

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