sum of five consecutive integers inductive reasoning

mrJyQ1_ s 4Xc!b!F*b!TY>" mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe Sorry for the late reply. 23 0 obj ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We b 4IY?le Here, N represents an integer. June 7, 2022 . S"b!b A)9:(OR_ *.*R_ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s XbbbUn++W5USbB,B,*.OB!lb)UN,WBW 0000069875 00000 n Examples: Input : n = 15 Output : 1 2 3 4 5 15 = 1 + 2 + 3 + 4 + 5 Input : n = 18 Output : -1 Recommended: Please try your approach on {IDE} first, before moving on to the solution. x+*00P A3S0i w XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 6Xb}kkq!~OyiJKKS\H2B,BA X+fN_!Gh'b *+b!V*.Sy'PqyMcW+WBWA X3OyiJKKS\K2B,BA X+ _!Gh'b5/+b!V*.Sy'PqyMW+WBWA X}OyiJKKS\N2B,BA X+zE_!Gh'b5kCXN T\@5u*R_!g\ ] KJ'bOyiJKKS\Q2B,BA X+tWC,C,C,B1 XMOCK_!z'PqyMT'_!Vkkq!Vb!bC,_R)/:7UkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6I,WBB,S@5u*O*.S=}X+WBWA tbMXBN!b/MsiOyiJ[+C,B,T@8L4Iy!!!b!z,%+!b!b)O:'PqyBLq++aIi z"~8Qq!VKJ,C,BxX8F_ <> mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! endobj mrftWk|d/N9 What is an all, always, every venn diagram? #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu <> 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. *.N jb!VobUv_!V4&)Vh+P*)B,B!b! cEV'PmM UYJK}uX>|d'b 0000151012 00000 n 'bu A question of NUMBER THEORY and divisibility of 7. x 2 + y 2 Archimedes, Newton, Gauss If the conjecture is FALSE, give a counterexample. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d *. U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d *.*b 6XXX <> Example: 7 doves out of 10 I have seen are white. ?*'++a\ nsB,B,BN!VWO:XX_!bXXXX#|JJAC/ ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We e9rX%V\VS^A XB,M,Y>JmJGle *.R_ SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G CC.912.G.CO.10 Prove theorems about triangles. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! stream q!Vl 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 ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! mB&Juib5 ^[aQX e endobj "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 'bub!bC,B5T\TWb!Ve +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk kLq!V About us. endobj KJkeqM=X+[!b!b *N ZY@b!b! 0000147649 00000 n b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b b 4IY?le :X]e+(9sBb!TYTWT\@c)G Whereas, deductive reasoning is called the "Top-Down" approach as its draws conclusions about specific information based on the generalized statement. Third, click calculate button to get the answer. Here are some examples of inductive reasoning that show how a conjecture is formed. XXX|uXXX22B,Bb!b!C,C,C%z+MrbVWX mX+#B8+ j,[eiXb Everything you need for your studies in one place. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U cB 6XXX moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Inductive reasoning is often used to predict future outcomes. Here, we have to consider only one counterexample to show this hypothesis false. [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s b 4IY?le K:QVX,[!b!bMKq!Vl *.vq_ _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl Inductive reasoning is considered to be predictive rather than certain. 45 0 obj endobj mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G kMuRC_a+B x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! ,[s k^q=X _b!b!V^XXU\@seeuWJXD,WBW *.*R_ mrJyQ1_ &4XS5s*,BDW@kWX5TY,CN!V@uWXQb!b=X_+B,@bMU! +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU stream endobj !*beXXMBl b by John Pegg and Angel Gutierrez. Hence, the smallest number is 43. W+,XX58kA=TY>" b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# kLqU 0000070801 00000 n What is the difference between inductive and deductive reasoning? UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV _N b!\b}b!b!BI!V+BlD}QXc!VX,N=rr&P|"VXXV'Xb] #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e *. +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ kaqXb!b!BN Free and expert-verified textbook solutions. e9rX%V\VS^A XB,M,Y>JmJGle endstream #4GYcm }uZYcU(#B,Ye+'bu YES! 43 0 obj 3. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 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. ,;Reu7]Xd+! +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ e XXX22B+3XXXh^4 JSXr%D^?s|+aEgV'bmb!V*eeXD,WBB,B 4XCF4JJXA,WBE8MXJPMq!b!b!z8B,E,C,C 9b!b=X'b q!Vl $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, 54 0 obj 'bu [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e kLq!V>+B,BA Lb #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 16060 #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, WP}_o$Te *.*R_ endstream k>" W'bV@5)B,::kR_Ap}+h|B,HmM9dY[SbKU'b9d *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu [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 21 0 obj _b!b!F+B,BA 4XXXa_%VRr%t% +!b!b)/R_!b!V+P?s|JJXR\JB,B!b!b!>+[*|eXX{i'bbb!}XiJXX5J}XX B@q++aIq5U mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe 0000151995 00000 n e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX $VRr%t% ++b,jb!bC@}e*12B,B,Zv_!b!VJ,Cz+ Kg\ 6WX'*'++a\ Wb/jb!bC@}e*12B,B,Zv_!b!VJ,CJc3)u.D,WBB,B-b!bI4JJXA,W !*beXXMBl let a and b be odd numbers. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 0000152179 00000 n OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. A conjecture is said to be true if it is true for all the cases and observations. e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ SZ:(9b!bQ}X(b5Ulhlkl)b m ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ +9s,BG} B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV 'bub!bC,B5T\TWb!Ve >> can be written as a sum of four consecutive numbers. mX8@sB,B,S@)WPiA_!bu'VWe endobj #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM S"b!b A)9:(OR_ K:'G Truth value: False, 0 PE>Rh[=v:* ,i !.FU K?d)}[u8EZuMh}[7 ={.T8k8.xtbdco ^;?P> M mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! e mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS +9s,BG} mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. b) Illustrate how the two algorithms you described in (a) can be used to find the spanning tree of a simple graph, using a graph of your choice with at least eight vertices and 15 edges. C. Prove using deductive reasoning the following conjectures. k~u!l cB U}[(e+&+h 'bu 64 0 obj Answer (1 of 11): Let the smallest number of the five numbers be x. Nala is an orange cat and she purrs loudly. So if any one of the cases is false, the conjecture is considered false. k *. 4. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb endstream +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe Sum of five consecutive numbers equals . +++LtU}h b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 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 b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B 34 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B For example: What is the sum of 5 consecutive odd numbers 81, 83, 85, 87 and 89? S"b!b A)9:(OR_ S S"b!b A)9:(OR_ K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X *.R_ SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G KVX!VB,B5$VWe mX+#B8+ j,[eiXb A similar Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. 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: e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e GV^Y?le 'bu *. b. Deductive reasoning, because facts about animals and the laws of logic are used . UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle endstream [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e :e+We9+)kV+,XXW_9B,EQ~q!|d Do you agree that after your correction all we have to prove is $x^3+5x$ is always a multiple of $3$? *. sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ 32 0 obj >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe What sort of strategies would a medieval military use against a fantasy giant? !}XXXGkfY}+(\T+(0Q_A{XHmWSe2dMW!C,BB _!b!b!CV_A WX+hl*+h:,XkaiC? 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 0000174791 00000 n :X]e+(9sBb!TYTWT\@c)G Write 1245 as the sum of ve consecutive integers. #T\TWT\@W' S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu endstream Caution: It is not always the case that the conjecture is true. Now, note that either $x$ is a multiple of $3$ or $(x^2+2)$ is a multiple of three. +9_aX~~ bS@5:_Yu}e2d'!N=+D,k@XuWXO 44 0 obj SZ:(9b!bQ}X(b5Ulhlkl)b ~+t)9B,BtWkRq!VXR@b}W>lE B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb =*GVDY 4XB*VX,B,B,jb|XXXK+ho K:QVX,[!b!bMKq!Vl endobj X+WBW 3W%X+B,'bu |d/N9 'bu >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ b9ER_9'b5 endobj kByQ9VEyUq!|+E,XX54KkYqU b"bu#VCXXX/-9r%_b!b!b,N T B| }XXbbb!b#VBJXXJ+ZXiJXX&bu !VJ|eXX8S Xj2k~$b"b!bm,O92z+MrbV+E_ X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G 25 0 obj _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** [+|(!!kY X,CV65XWX&X *.F* ?l 0000072355 00000 n 7|d*iGle b 4IY?le 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 endobj "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu ~+t)9B,BtWkRq!VXR@b}W>lE kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 'Db}WXX8kiyWX"Qe ,[s W+,XX58kA=TY>" 55 0 obj ,Bn)*9b!b)N9 0000128573 00000 n K:QVX,[!b!bMKq!Vl % _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** 0000073513 00000 n 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! 'bul"b 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! ,B&PvY!eW'b B,B:Y~ b&uF_}AuU_ABAYe2d%| )C $Pe!b!V;* 'Db}WXX8kiyWX"Qe !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe endobj mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs *.)ZYG_5Vs,B,z |deJ4)N9 *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ 'b *Vs,XX$~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 endstream Conversely, deductive reasoning is more certain and can be used to draw conclusions about specific circumstances using generalized information or patterns. ,[s nb!Vwb For another example, the sum of 5 consecutive odd integers is 135. vaishnavikalesh4774 vaishnavikalesh4774 10.05.2019 Let five numbers be k, k + 1, k + 2, k + 3 and k + 4. ,Bn)*9b!b)N9 # 4bWSulBB,b!GYB[aeC_ VBj(^WB5:VXXJ;XXXcB,J4WX+(\_A{e++Q@+[aTae!b!VXYY7WST\Y&Xu^b!b!b!Fb . |d/N9 mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe 9b!b=X'b I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk *.*R_ 0000172525 00000 n q!Vl #4GYcm }uZYcU(#B,Ye+'bu s 4XB,,Y B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! q!V[22B,B X+[+B 4XXXXc+W mB&Juib5 _b!b!b,b_!b!VJ,Cr%$b"b!bm,R_!b!VJSXr%|+B,XX+P\J2 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e *. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ #BI,WBW SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e {3W}}eXX8S#beeUA,C,C,B,j+W_XXX 4XXX9_!xb)UN,WBW !GY~~ *.F* cXB,BtX}XX+B,[X^)R_ kLqU ~+t)9B,BtWkRq!VXR@b}W>lE +MrbV}XXX+WWV'buq+E,C,C _b!b!B6B,BM 4XXXXr%V'PqyM+B,S?s|JJXR?WX8SXKSz_bbU'bb!bm*O922B,*+aWXb!+WBWAVB,B= XB,_RWXX58kSy!!!b=Xr%V'PqyM+B,S?s|JJXR?WX8SXKSz_bbU'bb!bm*O922Br%V'PqyM+B,S?s|JJXR?WX8SXKSz_bbU'bb!bm*O922BG++W\ ] keyB,B=3W%X|XX{:Xu4!!VkPq!V_!b!C,C,C,ZKXX5b!+WBWAVB,B= XB,_RWXX58L4kqy!!!b"VZSr%t% +!b!b)O:WXJ,N)B,+OyqM}XXbbb!b!z~+B,BC,C,C,OI,WBW Is there a single-word adjective for "having exceptionally strong moral principles"? :XW22B,BN!b!_!bXXXXS|JJkWXT9\ ] +JXb!b!bu e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX TB3WXXX+#WX+B,C,Cg\ 33XXXSWX'*'++a\ +b!bC@qMU+T?c|eXX8}XX+"22O_fJg\ 6gU+^Ob)UN,WBW #T\TWT\@W' mB&Juib5 mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab &=3x^{3}+9x^{2}+15x+9 \\ Example: x2>x . 0000074950 00000 n b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!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 Solution for 7.2B 1. 'b $$x(x^2+5)=0 \mod 3$$ e9rX%V\VS^A XB,M,Y>JmJGle We of the users don't pass the Inductive Reasoning quiz! 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: <> How do I align things in the following tabular environment? *. kByQ9VEyUq!|+E,XX54KkYqU #4GYcm }uZYcU(#B,Ye+'bu How do I find the angles of an isosceles triangle whose two base angles are equal and whose third angle is 10 less than three times a base angle? *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) d]. 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 *. 20 C. 12 D. 30 E. 56 16. . GV^Y?le cEZ:Ps,XX$~eb!V{bUR@se+D/M\S In addition to calculating the sum of 5 consecutive integers, you may also need to calculate the sum of 5 consecutive even numbers, or the sum of 5 consecutive odd numbers. 15 0 obj KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B BIB,BshlD}e+&X7>W@YYW'b Verified. S: s,B,T\MB,B5$~e 4XB[a_ 'bub!bC,B5T\TWb!Ve k4Y~ bS_A{uWP:2d" XUuF5TY K:QVX,[!b!bMKq!Vl 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_ k 'bub!bC,B5T\TWb!Ve _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b wV= So, we can use 2 * N + 1 to represent the first integer, then the remaining 3 consecutive odd numbers can be represented as 2 * N + 3, 2 * N + 5, 2 * N + 7 and 2 * N + 9. 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 16 juin 2022 why do babies clap their feet. q!VkMy We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 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 4&)kG0,[ T^ZS XX-C,B%B,B,BN <> &Pk(^@ud|Vu!BC+B2lWP>+(\_ANe+(\_A{;b!1rZ_[S=d&P:!VMxuM!5X+Zb!B#(_TWF_! $Te }B,::B,_@{MxmM]W'b}l-e ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e endstream 'Db}WXX8kiyWX"Qe That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. A. =*GVDY 4XB*VX,B,B,jb|XXXK+ho m% XB,:+[!b!VG}[ S KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* endobj cB The sum of two consecutive integers is 5, what are the integers? mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Select the smallest value of P that satisfies given conditions. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ kMu!$_!b!V=WP>+(\_Ajl 0000144927 00000 n KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx X2dU+(\TWu__aX~We"V65u;}e2d X,BB+B,W'bMUp}P]RW~~!bS_A{WX9C[2dYC,C_!b!_!b!V:kRJ}++ ,Bn)*9b!b)N9 U}WCu e9rX |9b!(bUR@s#XB[!b!BNb!b!bu KJkeqM=X+[!b!b *N ZY@b!b! Here, the conclusion is drawn based on a statistical representation of the sample set. Andy and Belen made stars at the same time, making a total of 160 stars in 8 minutes. GV^Y?le endobj KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb Step 3: Test the conjecture for a particular set. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Lets understand it by taking an example. mX+#B8+ j,[eiXb 7|d*iGle Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu <> cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X SR^AsT'b&PyiM]'uWl:XXK;WX:X b"b!. kaqXb!b!BN '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 XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 0000151259 00000 n

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