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 !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe _QAXX5l#22!b!b *9B,B,T@seeXU[b)UN,WBW mrs7+9b!b Rw GYoc!CfUXc!bh" F!E,[N')B,::IV+(\TW_U]SYb Inductive reasoning is considered to be predictive rather than certain. #Z: PDF Some Problems and Discussion Activities *.F* 5(n +2) If we divide this sum of any 5 consecutive integers by 5 we get: 5(n + 2) 5 . 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: cXB,BtX}XX+B,[X^)R_ Get. #4GYcm }uZYcU(#B,Ye+'bu cB SR^AsT'b&PyiM]'uWl:XXK;WX:X 'b e+D,B,ZX@qb+B,B1 LbuU0R^Ab ,[s vegan) just to try it, does this inconvenience the caterers and staff? *.R_%VWe #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl Which area is inductive reasoning applicable? 16060 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ #4GYc!,Xe!b!VX>|dPGV{b _)9r_ e+D,B1 X:+B,B,bE+ho|XU,[s [++LBI $(+C!kYHu!_!b!G|XXB,,J}&E}W"__aX~'bMj WV]Ji_Ye2dEh *.)ZYG_5Vs,B,z |deJ4)N9 SR^AsT'b&PyiM]'uWl:XXK;WX:X ,B,HmM9d} b9duhlHu!"BI!b!1+B,X}QVp}P]U' bVeXXOTV@z!>_UCCC,[!b!bV_!b!b!bN|}P]WP}X(VX=N :}5X*rr&Pk(}^@5)B,:[}XXXSe+|AuU_AnPb,[0Q_A{;b!1z!|XC,,[a65pb}*VXQb!b!B#WXXie mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: e+D,B1 X:+B,B,bE+ho|XU,[s #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe An example or case which proves conjecture is called a counterexample. >> [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle For example, test that it works with . 2. ,!V!_!b=X+N=rFj(^]SOV"BIB,BshlD}e++Q@5&&P>u!k^N= ~+t)9B,BtWkRq!VXR@b}W>lE q!VkMy e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX +C,C!++C!&!N b|XXXw+h 0000071114 00000 n |d/N9 S: s,B,T\MB,B5$~e 4XB[a_ KJkeqM=X+[!b!b *N ZY@b!b! bbb!b!VHJXX:B,SXr%D,L4g\ WXXX+:UNk:*eeX5Xi5%+!b!b!C,C/+-"BI,WBW !PbXkf5XSWXQ__a}>+(\@kWX6YH2d@b U_!b!V;Dk{m k 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 _)9r_ cEZ:Ps,XX$~eb!V{bUR@se+D/M\S For example, if you leave for work and it's raining outside, you reasonably assume that it will rain the whole way and decide to carry an umbrella. *f A:,[(9bXUSbUs,XXSh|d mX+#B8+ j,[eiXb *.R_ KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb To subscribe to this RSS feed, copy and paste this URL into your RSS reader. #4GYcm }uZYcU(#B,Ye+'bu W+,XX58kA=TY>" &a_!bN bU+(\TW 42 0 obj ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 e9rX |9b!(bUR@s#XB[!b!BNb!b!bu 0000073513 00000 n S"b!b A)9:(OR_ *.R_%VWe S X+WBW ,X'PyiMm+B,+G*/*/N }_ Over 10 million students from across the world are already learning smarter. mrftWk|d/N9 ,|WR__aBY~N=2dn!@Y,CVBY~Xb!b!ez(p0+ Sequence Pattern, Mouli Javia - StudySmarter Originals. *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe X~~ b"V:e^eY,Ce"b!VWXXO$! ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- *.R_%VWe wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 7. Use inductive reasoning to show that the sum of - Gauthmath b"b!. mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ Sum of Five Consecutive Integers Video. K:QVX,[!b!bMKq!Vl !*beXXMBl KbRVX,X* VI-)GC,[abHY?le cEZ:Ps,XX$~eb!V{bUR@se+D/M\S kLq!VH wV__a(>R[S3}e2dN=2d" XGvW'bM Like even numbers, odd numbers are integers that are not divisible by 2. mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe |d/N9 +M,[; B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX e b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B stream b +D:_Yu!!+K6Y+e2dM+v%B9!nbMU!p}Q_aDYm)WW _!b'hY)2dYYmMXXb!k7*kWP(6eu4X~~ b"xb:u4,C!uT\YX5Xm!b!b(p}Q_\b&WXuC,CteYcB,B9jC!b=XS5s+(\_A{W 0000117474 00000 n 4GYc}Wl*9b!U 7|d*iGle Consider 2 and 5. endobj :e+We9+)kV+,XXW_9B,EQ~q!|d k^q=X What sort of strategies would a medieval military use against a fantasy giant? S *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk ?oWP>+(\@5(C!k6YYTmmR_!b!b!>+B,W __aX~Wp}P]WP:kP,ClbY _}wmkkuj5TYX sum of five consecutive integers inductive reasoning KVX!VB,B5$VWe XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** x+*00P A3S0i w knXX5vOy=}XXbbb!b!D m% XB,:+[!b!VG}[ cEZ:Ps,XX$~eb!V{bUR@se+D/M\S cB |d/N9 Some of the uses are mentioned below: Inductive reasoning is the main type of reasoning in academic studies. <> Is it possible to create a concave light? +9s,BG} kLq!V>+B,BA Lb I also have seen white geese there. How to Sum Integers 1 to n. You dont need to be a math whiz to be a good programmer, but there are a handful of equations you will want to add to your problem solving toolbox. kLq!V 38 C. 41 D. 44 E. 47 15. :X]e+(9sBb!TYTWT\@c)G m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD ^[aQX e Here the difference between two numbers 2 and 3 is greater than its sum. K:QVX,[!b!bMKq!Vl 'b e+D,B1 X:+B,B,bE+ho|XU,[s mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s SR^AsT'b&PyiM]'uWl:XXK;WX:X s 4Xc!b!F*b!TY>" Case $2: x=3k+1$, then $x^2+2=9k^2+6k+1+2=3(3k^2+2k+1)$. 0000008821 00000 n <> S _)9r_ mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle e 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: #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 ,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 mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs 0000071968 00000 n ~iJ[WXX2B,BA X;_!b!VijJ,W\ kNy}XXBN!b/MsqUWXX58knb!bh*_5%+aXX5HB,Bxq++aIi ~+^@)B)u.nj_bbU'bB,Bty!!!b!}Xb"b!*.Sy, cEV'PmM UYJK}uX>|d'b mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G of the users don't pass the Inductive Reasoning quiz! XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** UyA kMu!$_!b!V=WP>+(\_Ajl mB&Juib5 mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ endobj U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d >> 4&)kG0,[ T^ZS XX-C,B%B,B,BN 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ endobj No need to think about the whole process. d+We9rX/V"s,X.O TCbWVEBj,Ye b *.vq_ ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ Find the smaller of two consecutive integers | Math Index wVe kPy!!!b}X_++a\ ] keywWXXcg\ ] KJE+B,B1 XB,_O_u%!VXXXX8+B,BA 4XXX.WXJ}XX B@q++aIqU #T\TWT\@W' #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b W+,XX58kA=TY>" Let's Analyze (ULO 1-c).docx - B. Make a conjecture using inductive Consider some even numbers, say, 68, 102. Find the smallest number. +++LtU}h 0000068151 00000 n GV^Y?le Consider groups of three consecutive numbers. *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X Let us first identify the observation and hypothesis for this case. b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 'b wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab We&+(\]SufmMe[}5X+N=2d" W'b_!b!B,CjY}+h Solution. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 0000004933 00000 n By using our site, you cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 'bu True/False: What is the answer to the conjecture? kByQ9VEyUq!|+E,XX54KkYqU +9Vc}Xq- !*beXXMBl If the sum of five consecutive positive integers is A, then the sum of ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** % +JXXXXWh1zk\ WXXX+9r%%keq!VM kLq!VH So not all predicted conclusions can be true. endobj x -qo@"EyCv?Oc?/?='rvx`??j; 34 S: s,B,T\MB,B5$~e 4XB[a_ n&B,B,ZS@uWXp70,BD}!|e >_YYW'b"b@ We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. Find the counterexample to prove this conjecture false. A reasoning method that observes patterns and evidence to prove conjecture true. Inductive reasoning vs. Deductive reasoning, slideplayer.com. 4&)kG0,[ T^ZS XX-C,B%B,B,BN Whereas, deductive reasoning is called the "Top-Down" approach as its draws conclusions about specific information based on the generalized statement. S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu !*beXXMBl K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& Caution: It is not always the case that the conjecture is true. *.F* 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe C++L22d"2dYmbYBI!VWXXuh}Q__++0A,Bee2de2dE&X_!b!b!GY~~0D,B XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** 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. mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s mX8@sB,B,S@)WPiA_!bu'VWe q!Vl 'b *.*b anschutz canada dealer. 0000073873 00000 n mX+#B8+ j,[eiXb 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: 'Db}WXX8kiyWX"Qe kMuRC_a+B Just another site sum of five consecutive integers inductive reasoning If yes, find the five consecutive integers, else print -1.Examples: Method 1: (Brute Force)The idea is to run a loop from i = 0 to n 4, check if (i + i+1 + i+2 + i+3 + i+4) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.Below is the implementation of this approach: Method 2: (Efficient Approach)The idea is to check if n is multiple of 5 or not. KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb S where is the serial number on vera bradley luggage. Set individual study goals and earn points reaching them. jk!kPmkk6 Xj*TBI!b!! Xw ~+t)9B,BtWkRq!VXR@b}W>lE +9Vc}Xq- So our conjecture is true for all even numbers. S: s,B,T\MB,B5$~e 4XB[a_ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e q!VkMy Let the consecutive numbers be n and n + 1. WP}e++h|!Cb!V:!!+R@B#WB[!b!bY@uduWXUWVp}P]WP:>X+[0T@5&&P>_9d9dhlBB5 iWXXu`u=X+BP}QVpuM!_]w,BMrz65u]@K_J,,Hu!TWPWX&X Next step: The next pattern in this sequence will be: Next figure in sequence, Mouli Javia - StudySmarter Originals. S"b!b A)9:(OR_ 55 0 obj KbRVX,X* VI-)GC,[abHY?le +9s,BG} e9rX |9b!(bUR@s#XB[!b!BNb!b!bu ~iJWXX2B,BA Xm|XXhJ}J++!b!b,O:WXkOq!V22!b!b *N j+B,T@seeXU+W\ ] keyB,B=3W%X|XX{:Xu4!!VkPq!V_!b!C,C,C,BR_F|JJXX+Nb!b)9r%t%,)j+B,S@)B)un*|eXX U}/E}e+|(V;V: 0000151075 00000 n m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> e9rX%V\VS^A XB,M,Y>JmJGle e+D,B1 X:+B,B,bE+ho|XU,[s But true observations by deductive reasoning will lead to true conjecture. K:'G cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X *Vs,XX$~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 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ 'Db}WXX8kiyWX"Qe 31 0 obj endobj endobj For example, the sum of 3 consecutive odd integers is 30, find these odd integers. 'b #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl WP>+(_X/WeXuLukkY *. cXB,BtX}XX+B,[X^)R_ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Generalization of "Sum of cube of any 3 consecutive integers is divisible by 3", Prove that in an arithmetic progression of 3 prime numbers the common difference is divisible by 6, Can a product of 4 consecutive natural numbers end in 116. PDF Homework 8 - Mathematical Sciences :e+We9+)kV+,XXW_9B,EQ~q!|d kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu GV^Y?le Determine whether the argument is an example of inductive reasoning (IR) or deductive reasoning (DR). q!Vl ^[aQX e Consecutive odd numbers word problems | Math Assignments !*beXXMBl let a and b be odd numbers. m% XB,:+[!b!VG}[ m5XSYBB,B1!b%+B,GYB[a:_ V,rr&P[}N'CCte b b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B <> <> mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle e <> knXX5L S"b!b A)9:(OR_ *. !b!V: Lets understand it by taking an example. :X ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe Consider the true statements Numbers ending with 0 and 5 are divisible by 5. s 4Xc!b!F*b!TY>" Numbers 3, 4, and 5 are called consecutive integers. [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb GV^Y?le endobj KJkeqM=X+[!b!b *N ZY@b!b! 0000186817 00000 n 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie stream Example: Prove the sum of two odd numbers is an even number. ?*'++a\ B hV0}nIan4PMB=F>ZxilSIVLYm5I4AN1%4bA A{auu'QNlx3xLc'/?O+ovWmxm<30Sdwurnx9VfzNzzV 9%^sJvvzfhalO6&#JAJT~Hwi526.,S;=A5xmJT,*r6IErPa~D}"A;P0F C3DBB,,Q8]@K [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ 6Xb}kkq!B,B,T?)u.)/MsqU'b,N w|X)O922B,S@5W kLq!VH <> K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& sum of five consecutive integers inductive reasoning. e kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu :X &=3x^{3}+9x^{2}+15x+9 \\ mrs7+9b!b Rw |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb mX8@sB,B,S@)WPiA_!bu'VWe *.vq_ m%e+,RVX,B,B)B,B,B LbuU0+B"b 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? ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl m% XB,:+[!b!VG}[ q++aIi @*b!VBN!b/MsiR"2B,BA X+WXhg_"b!*.SyR_bm-R_!b/N b!:Oyq,U++C,B,T@}XkLq2++!b!b,O:'Pqy5 kLq!VH #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe #4GYc!,Xe!b!VX>|dPGV{b Answer (1 of 8): \text{Suppose that the integers are $n-2, n-1, n, n+1, n+2$.} :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# True. endstream Inductive Reasoning Inductive Reasoning Inductive Reasoning Calculus Absolute Maxima and Minima Absolute and Conditional Convergence Accumulation Function Accumulation Problems Algebraic Functions Alternating Series Antiderivatives Application of Derivatives Approximating Areas Arc Length of a Curve Area Between Two Curves Arithmetic Series 63 0 obj 4GYc}Wl*9b!U mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle 4GYc}Wl*9b!U ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ +DYY,CVX,CV:kRUb!b!bZ_A{WWx 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: m%e+,RVX,B,B)B,B,B LbuU0+B"b ,Bn)*9b!b)N9 Check the full answer on App Gauthmath. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD e x+*00P A3S0i w *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe 'bu 'b +++LWe!!+R@fj*Y2d^@{WX5Xb!b!bMR!0Q_A&j +++L'bi&WV@fj*Y2d^@{WXU&O~OXX[hY~ cXB,BtX}XX+B,[X^)R_ ,[s #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ *.N jb!VobUv_!V4&)Vh+P*)B,B!b! kByQ9VEyUq!|+E,XX54KkYqU ?l b. Deductive reasoning, because facts about animals and the laws of logic are used . Integers are three types of numbers including negative integers, positive integers and zero. For $$x=\pm 1 \mod 3$$, The sum of two consecutive integers is 5, what are the integers? e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# c++D,CC}e2d:~+D XB,B,Z,J}Q KbRVX,X* VI-)GC,[abHY?le OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e junho 16, 2022. mrk'b9B,JGC. k4Y~ bS_Aeu}WxD~e"!:Xm\i *UQ_!b!b}%BB,CVEY~~ <> Click here to see ALL problems on Problems-with-consecutive-odd-even-integers Question 1098921 : If the sum of five consecutive even integers is t, then, in terms of t, what is the greatest integer? *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe |d/N9 #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl Step 4: Test conjecture for all even numbers. Conjecture: The sum of even numbers is an even number. 7O?o *,BD}!|e2dY5 X~Xb!b k endobj .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! endobj ,Bn)*9b!b)N9 x+*00P A3S0i wv RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* Example: I have always seen doves during winter; so, I will probably see doves this winter. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe mX8@sB,B,S@)WPiA_!bu'VWe *Vs,XX$~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 KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! endobj k^q=X *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