kaqXb!b!BN mrs7+9b!b Rw cB B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 'bu XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** ,[s b9ER_9'b5 Sum of the smaller and twice the larger is -4. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: S *.vq_ endobj Therefore, let the first even number is 2 * N, then the remaining 4 consecutive even numbers can be expressed as 2 * N + 2, 2 * N + 4, 2 * N + 6and 2 * N + 8. 0000055055 00000 n + +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk sum of five consecutive integers inductive reasoning Isgho Votre ducation notre priorit WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d KJkeqM=X+[!b!b *N ZY@b!b! VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s Example: I have seen white doves in the park. 0000172261 00000 n _WX B,B,22 !!b!b-6'bbb &VWmT9\ ] +JXXsZ+B,jbg\ ] KZ+B,jb!b!bmUbbbUWXXh+JSXr%D,B9-b!b53W%b!b5**eeXX+B,B 4XXXb)UN,WBW B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb S 0000094336 00000 n |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb ~+t)9B,BtWkRq!VXR@b}W>lE 0000057583 00000 n B,_!bD&Pzj(^[S N="b!B#+B,ZT@p}[GYB XGV'P cEZ:Ps,XX$~eb!V{bUR@se+D/M\S mrJyQ1_ _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** *. #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe m%e+,RVX,B,B)B,B,B LbuU0+B"b Then state the truth value ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl +9s,BG} :X]e+(9sBb!TYTWT\@c)G *.N jb!VobUv_!V4&)Vh+P*)B,B!b! cB +9Vc}Xq- |d/N9 True statement My dog is brown. 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: b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# CONTACT; Email: Inventory Management Strategies Of Canadian Tire, How To Create 15 Minute Time Intervals In Excel, New Balance Indoor Nationals 2022 Standards. *. 16060 XXXSXXX22B,BUSbB,B,*.O922jJbMMbVtWXXB,B!b!b!}bbbUvWMNBI,WBW b 4IY?le MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 0000167617 00000 n cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ <> wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! Write the inverse, converse, and contrapositive of the conditional statements below. 9b!b=X'b +9s,BG} 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu UyA MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie #4GYcm }uZYcU(#B,Ye+'bu JSXr%|0B,B,B,B,z@N T\?c|eXX5wj5UWbbEeeuWO VR)/Ir%D,B,;}XXLb)UN,WBW Select the smallest value of P that satisfies given conditions. +9s,BG} C. Prove using deductive reasoning the following conjectures. W+,XX58kA=TY>" I thought of doing a proof by contradiction. What sort of strategies would a medieval military use against a fantasy giant? #T\TWT\@W' junho 16, 2022. b 4IY?le 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 mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! SZ:(9b!bQ}X(b5Ulhlkl)b Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. U}E}b,[0Q_A{;XX|B,P@{MxmM]WRWO8d *.R_ (b) Write 1346 as the sum of four consecutive integers. About us. KVX!VB,B5$VWe *. 0000127387 00000 n #4GYc!,Xe!b!VX>|dPGV{b _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! It's true when $x=0 \mod 3$. 0000003474 00000 n +9s,BG} b kByQ9VEyUq!|+E,XX54KkYqU mrk'b9B,JGC. Caution: It is not always the case that the conjecture is true. endobj m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> ?l $(x-1)^3+x^3+(x+1)^3=3x^3+6x=3(x^3+2x)=3x(x^2+2)$. *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe K:'G +++L'bi&WV@fj*Y2d^@{WXU&O~OXX[hY~ Then the numbers are x, x + 1, x + 2, x + 3, and x + 4. #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b d+We9rX/V"s,X.O TCbWVEBj,Ye kLq!V :X S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu The difference between inductive reasoning and deductive reasoning is that, if the observation is true, then the conclusion will be true when using deductive reasoning. mrJyQ1_ ,X'PyiMm+B,+G*/*/N }_ 2021-04-26. endstream 16 juin 2022 why do babies clap their feet. endstream S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu $VRr%t% ++b,jb!bC@}e*12B,B,Zv_!b!VJ,Cz+ Kg\ 6WX'*'++a\ Wb/jb!bC@}e*12B,B,Zv_!b!VJ,CJc3)u.D,WBB,B-b!bI4JJXA,W U}[(e+&+h XXX22B,}r%t%XXU\@se^_!b'VRr%t% +!b!V+B,B,bg~%SXXb!V*eeX!}JJCO Find the next 5 terms in the sequence 38, 31, 24, 17, ___, ___, ___, ___, ___ . b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# Let us first identify the observation and hypothesis for this case. Here, N represents an integer. For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? 25 0 obj mX+#B8+ j,[eiXb _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L Inductive reasoning is used in academic studies, scientific research, and also in daily life. Andy made 4 more stars per minute than Belen. mX+#B8+ j,[eiXb cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU |d/N9 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe ,X'PyiMm+B,+G*/*/N }_ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X Determine whether each equation is true or false. |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 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: kByQ9VEyUq!|+E,XX54KkYqU #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl m%e+,RVX,B,B)B,B,B LbuU0+B"b !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe 0000174791 00000 n #4GYc!,Xe!b!VX>|dPGV{b 7|d*iGle q!VkMy b9ER_9'b5 bbb!b!V_B,B,*.O92Z5k\ WXXX+9r%s%l+C,B,B Xzn Are inductive and deductive the same type of reasoning? b 4IY?le =k4^`e!b=X+N=rFj(L_M% Example: x2>x . kLq!VH mX+#B8+ j,[eiXb Explain who is correct and why. UyA 69 0 obj kByQ9VEyUq!|+E,XX54KkYqU m% XB,:+[!b!VG}[ wl|k^Mx rr,hlX_ B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX *. endobj #Z: +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU 4&)kG0,[ T^ZS XX-C,B%B,B,BN 'bu KbRVX,X* VI-)GC,[abHY?le [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L This. ,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 LwwvX,WyS18g]Qt'zi``{Xfo7=H8SS 0my*e| endobj mB&Juib5 Prime numbers only have two factors, 1 and itself, If prime numbers only have 2 factors, then they are 1 and itself. 72 0 obj 34 cB C,C,C,B1 X3}uXX5b}[?s|JJXR?8=B,B,B>S^R)/z+!b!D k^q=X Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? 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: The use process is also very simple, input the first integer, then select the integer type. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 0000151454 00000 n :XW22B,BN!b!_!bXXXXS|JJkWXT9\ ] +JXb!b!bu |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s endobj d+We9rX/V"s,X.O TCbWVEBj,Ye <> Six consecutive integers equal 27 when added together. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S There are 10 consecutive nonzero positive integers. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD >> k^q=X So, the statements may not always be true in all cases when making the conjecture. 4&)kG0,[ T^ZS XX-C,B%B,B,BN #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 *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G |d/N9 'bu kLq!V>+B,BA Lb #4GYc!,Xe!b!VX>|dPGV{b What is the third number? #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ [++LWe!!+R@zoeZ,C X~X+B,::I9dp}P]5Ww0A,w+hMxmM!*CVX,CV:@bAXXV'35UY3fNb&WN}Qb" ~Yse2dEh 43 0 obj <> #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 OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e endobj k^q=X mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* SInce there are 5 integers, 5x5 would make the sum 25 greater than A. #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d ,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 *.F* _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e m%e+,RVX,B,B)B,B,B LbuU0+B"b ,X'PyiMm+B,+G*/*/N }_ S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu *.F* k~u!B,[v_!bm= 0000067794 00000 n 0000057079 00000 n 0000066998 00000 n 6XXX kMuRC_a+B ):bKU'bYumkBXO!!k}P]5WcGY~~ ,B,HmM9d} b9duhlHu!"BI!b!1+B,X}QVp}P]U' bVeXXOTV@z!>_UCCC,[!b!bV_!b!b!bN|}P]WP}X(VX=N :}5X*rr&Pk(}^@5)B,:[}XXXSe+|AuU_AnPb,[0Q_A{;b!1z!|XC,,[a65pb}*VXQb!b!B#WXXie e9rX%V\VS^A XB,M,Y>JmJGle e |d/N9 ^[aQX e [5_bn~3;D+dlL._L>; ,S=& endstream endobj 365 0 obj <>stream ?l #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 67 0 obj kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb XGV'P|;b!VXYYumh^C0U@5)B,::&e_!b!b! 7|d*iGle mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs [++LBI $(+C!kYHu!_!b!G|XXB,,J}&E}W"__aX~'bMj WV]Ji_Ye2dEh *. Example: Prove the sum of two odd numbers is an even number. #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 C,C,C,B1 (bMb"b!*.Sy'PqyVWX_bm-N[_!b!b!V)/MsiOyqY}XXXkIq=X?b!7 4XXXXch=&\ kNyB,kkqm&[B,B,B>S^R)/z+!b!J e 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe Case $2: x=3k+1$, then $x^2+2=9k^2+6k+1+2=3(3k^2+2k+1)$. mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle GY~MxmM~W,Ce^N=2d"b}XXT'bMUp}P]5W~-e&+h This is opposed to a deductive reasoning Deductive Reasoning is the process of reasoning to a specific conclusion from a series of general statements. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. *.*R_ endobj cB >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 4&)kG0,[ T^ZS XX-C,B%B,B,BN Just because all the people you happen to have met from a town were strange is no guarantee that all the people there are strange. 6XXX [+|(!!kY X,CV65XWX&X If there is no solution, output -1. You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case. !*beXXMBl b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B #4GYcm }uZYcU(#B,Ye+'bu D:U!_;GY_+ZC,B e 4&)kG0,[ T^ZS XX-C,B%B,B,BN #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ >> m% XB,:+[!b!VG}[ +DHu!!kU!@Y,CVBY~Xg+B,XGY~#~mYO,B C++L'bMj WV@!e+zu!_!b!}XX:V)!R_An__aHY~~BI $j(}2dY}e^N=+D, ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We b 4IY?le ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b endobj endobj ^[aQX e Consider some even numbers, say, 68, 102. mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 0000053628 00000 n XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> Now here is how I try to do it. +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU bbb!b=XiDXXXh^Jk9*'++a\ +'B,B,B/_UV'buvB22 !!b!~b +!b!b!C,CrbX"VRr%t% +!b!DbX!B,ZR?s|JW%2B,B,ZY@^B)22 !!b!Nb&+!b!b!C,CbX%VRr%t% +!b!bX-B,ZR?s|JW%2B,B,ZY@+m$H,C,C 2d++Lu_+(\@5(C!k6YYTmmR_!b!b!b!be+L0A x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! ,[s kByQ9VEyUq!|+E,XX54KkYqU 2. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb kLq!V>+B,BA Lb S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu stream .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ Sum of Five Consecutive Integers Video. C+|AuU_AB3je&PYguu=Xm8Q@5)B,::A!Y!e&+(\TWN :3BYHmkkufmM]W'jc XB,BC(_TR__aAuU_AB3+e&PYguuD6nN b!bR@zWoWe&+(\TWN :3BYHmkkufmM]W'vbQtsu!#,z(0Q_Apu!bee2dEj(^[S3kk:6 `u!#,z(0Q_Apu!bee2dEj(^[S3kk:G?+([@5)B,::A!F_O,C_aX~WP>+(\@$!u_! Yk(^[S3k *Vs,XX$~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 X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d Multiple Choice Which of the following is a counterexample of the conjecture below? *. <> Where does this (supposedly) Gibson quote come from? 4&)kG0,[ T^ZS XX-C,B%B,B,BN ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu c++D,CC}e2d:~+D XB,B,Z,J}Q 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ kLqU _)9r_ Let us understand it by taking an example. Example #4: Look at the following patterns: 3 -4 = -12 To To prove that a conjecture is true, you need to prove it is true in all cases. d+We9rX/V"s,X.O TCbWVEBj,Ye S"b!b A)9:(OR_ 9b!b=X'b I. Download Free PDF Download PDF Download Free PDF View PDF. e endobj +++LtU}h VXT9\ ] +JXYb^_!,9z/+Cb!b!b!bXb-"22 !!bu'}JjJ_XXX 4X|X+BJSXr%DCB!b!b!bY?s|=b}WX3B,B,B,%}XB*eeX)_.b!b!Vqy!5_!k6*'++a\ 5kEXXXo_.+Cb!b!b!b'|XB*eeX]e_.b!b!Vqy!5_!k6*'++a\ XW|X+B,B,B,z/k~XXXXw+ZbEeeUA,C,C,J\ WMkE5XiJXuX}X+B,B,B,z+Cb!b!b!bub-"22 !!bXer%\PC_5%V/,B,BjK:_!k6*'++a\ *bygXXXW XXX cB cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ Consider groups of three consecutive numbers. :X+W:XXeeUA,C,C,Bm_vB,B,*.O92z+MrbVS(9r%SX5Xo For example, test that it works with . _)9r_ \end{align*}, This can be used to deductively prove that the sum of cube of $3$ consecutive numbers is divisible by $3$ but I can't prove it is divisible by $9$. p}P]WPAuUOQ_ b 4IY?le mX+#B8+ j,[eiXb X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d 41 0 obj cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ Lets understand it by taking an example. *. cEV'PmM UYJK}uX>|d'b m%e+,RVX,B,B)B,B,B LbuU0+B"b <> mrk'b9B,JGC. e kaqXb!b!BN 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! The sum of any two consecutive integers is always odd. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G KVX!VB,B5$VWe 0000005175 00000 n endobj log(x1)log(x+2)=log(x+2)log(x1). *. The sum of three odd integers. =*GVDY 4XB*VX,B,B,jb|XXXK+ho Complete the conjecture: The square of any negative number is ? endobj *.N jb!VobUv_!V4&)Vh+P*)B,B!b! #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ k Here, our statements are true, which leads to true conjecture. *.*R_ Uu!:vC,C!+R@z&PC__!b!b-N :AuU_DQ_=++LWP>$QCC,C!+R@z&P&U'bZ_AYoWe&+(\TW XGk;}XoU'bYC65u^_!b!b-N :AuU_JQ_=++LWP>>[[SYo vkYe&+(Oo~>+(\@kWX5TY,C knXX5L GV^Y?le mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 66 0 obj OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 65 0 obj mrk'b9B,JGC. K:QVX,[!b!bMKq!Vl 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 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B 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%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs 'bub!bC,B5T\TWb!Ve UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. kaqXb!b!BN =*GVDY 4XB*VX,B,B,jb|XXXK+ho #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ KJkeqM=X+[!b!b *N ZY@b!b! Is it possible to create a concave light? b 4IY?le S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ cXB,BtX}XX+B,[X^)R_ endstream +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU Consider the true statements Numbers ending with 0 and 5 are divisible by 5. KJkeqM=X+[!b!b *N ZY@b!b! B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 0000004910 00000 n Translate into an equation. _b!b!V^XXU\@seeuWJXD,WBW Consider the following group of small even numbers. What can you say about the sum of any two odd integers? Inductive reasoning is considered to be predictive rather than certain. 1. mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ K:QVX,[!b!bMKq!Vl n&B,B,ZS@uWXp70,BD}!|e >_YYW'b"b@ This reasoning gives a chance to explore the hypothesis in a wider field. The type can be consecutive integers, consecutive even numbers or consecutive odd numbers. 3W%Xc+^@)B)u.j_bbU'bB,Bty!!!b!}Xb"b!*.Sy8 Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The sum of five consecutive integers is 100. find the third number. 0dfjWP(0Q_Az&Y!:_Yu!!MxmM]W'bMB,B,R@$AuL_ m% XB,:+[!b!VG}[ !*beXXMBl mB#V_!W'bZ_Ap7|b The sum of 5 consecutive integers can be 100. #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ ~+t)9B,BtWkRq!VXR@b}W>lE 'bu q!VkMy SZ:(9b!bQ}X(b5Ulhlkl)b e+D,B1 X:+B,B,bE+ho|XU,[s B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX In this tutorial, you learned how to sum a series of consecutive integers with a simple and easy to remember equation. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Truth value: True. b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B endobj *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* _b!b!b,b_!b!VJ,Cr%$b"b!bm,OR_!b!VJSXr%|+B,XX+P\G2 kLq!VH +9Vc}Xq- |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! S: s,B,T\MB,B5$~e 4XB[a_ DXX 6JzYs-m65292023591 - > > ()4~7 . #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 cEV'PmM UYJK}uX>|d'b ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! EXAMPLE 1. 49 0 obj mrs7+9b!b Rw ~+t)9B,BtWkRq!VXR@b}W>lE !V2 mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 5_!b!bNU:~+WP}WWR__a>kRuwY,CV_Yh _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 'bu K:'G 33 e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX 0000071114 00000 n w0dV+h _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b ,Bn)*9b!b)N9 mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe =*GVDY 4XB*VX,B,B,jb|XXXK+ho KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 'bul"b +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU ?l 7|d*iGle Then use deductive reasoning to show that the conjecture is true. |d/N9 6XjBwj?+WBWA X++b!V)/MsiOyiJK 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ SZ:(9b!bQ}X(b5Ulhlkl)b kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG kaqXb!b!BN x 1 (x 1 1) 1 (x 1 2) 1 (x 1 3) 1 (x 1 4) 5 __?__ 22. Uu!b'}; XcI&Pzj(^[SC[ XBB,ZS@}XX:AuU_A K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& e9rX%V\VS^A XB,M,Y>JmJGle W+,XX58kA=TY>" nb!Vwb w,[0Q_AN O buj(^[S=d >_9d9dhlBB5 4X?+B,B,::AuU_A e+D,B1 X:+B,B,bE+ho|XU,[s WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d ~iJ;WXX2B,BA X}+B,J'bbb!bUSbFJXXsNAub!b)9r%t%,)j? S: s,B,T\MB,B5$~e 4XB[a_ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk '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!V: UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV K:QVX,[!b!bMKq!Vl The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. stream mB&Juib5 42 0 obj +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe . endobj mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G Solution. 'bu e mX+#B8+ j,[eiXb UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV ,[s cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ A place where magic is studied and practiced? 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe K:QVX,[!b!bMKq!Vl mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b K:QVX,[!b!bMKq!Vl 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. =*GVDY 4XB*VX,B,B,jb|XXXK+ho UyA Difference between consecutive perfect squares 22- 42= 4 - 16 = 2 The difference between consecutive perfect squares is odd. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ Do you agree that after your correction all we have to prove is $x^3+5x$ is always a multiple of $3$? 0000069485 00000 n *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe 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 #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b 12 0 obj cEZ:Ps,XX$~eb!V{bUR@se+D/M\S cXB,BtX}XX+B,[X^)R_ ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b >> KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV 'b m%e+,RVX,B,B)B,B,B LbuU0+B"b ~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, 'bul"b This is similar to statistical induction, but additional information is added with the intention of making the hypothesis more accurate. *.R_%VWe mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Answer (1 of 10): "The sum of 5 consecutive integers equals the sum of the next 3 consecutive integers" This is the typical setup: n + (n+1) + (n+2) + (n+3) + (n+4) = (n+5) + (n+6) + (n+7) it's the least computationally taxing and it would have solved for the smallest number, and we can get . ZXW~keq!F_!bXXXXS|JJ+)BJSXr%D+N)B,B,B,qqU+aQo_b!b!b,N +B"bbbUk\ ] a!b!b'b5bX5XiJXXq>!b!bC,j^?s|JgV'bmb!V*eeXO'VZM(Ir%D,B,X@sbXXiJXXq2!b!b endobj ^@{eYmV2dYee"bG6kVe__A{WX5%__aX~~UN=2du6Ye2d+D,:XmD!b!b,CV(K0A,BBzu!!!k,YCV[Sqe"b%VNXX)U=++ *. :X SR^AsT'b&PyiM]'uWl:XXK;WX:X x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! mX8@sB,B,S@)WPiA_!bu'VWe !*beXXMBl Write 1245 as the sum of ve consecutive integers. :X]e+(9sBb!TYTWT\@c)G *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe SR^AsT'b&PyiM]'uWl:XXK;WX:X #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb G stream +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe XXXMl#22!b!b *n9B,B,T@seePb}WmT9\ ] +JXXsWX UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs *. kaqXb!b!BN Obviously, we have to find out these 5 consecutive integers before we can calculate their sum. [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 mX8@sB,B,S@)WPiA_!bu'VWe endstream #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 b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B What are the disadvantages of applying inductive reasoning? #T\TWT\@W' KVX!VB,B5$VWe 0000006113 00000 n m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L 3W%X+B,'bu <> *. 0000071968 00000 n 0000054543 00000 n b>X+B,XX+P\D2 Top Questions. B,B:Y~ b&uF_}AuU_ABAYe2d%| )C $Pe!b!V;* k^q=X k^q=X vaishnavikalesh4774 vaishnavikalesh4774 10.05.2019 3. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X *.N jb!VobUv_!V4&)Vh+P*)B,B!b! 7|d*iGle q!VkMy (By adding two more to the previous number you will get the next Q10. endobj Use inductive reasoning to show that the sum of five consecutive integers . #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 0000008844 00000 n Here, the conclusion is drawn based on a statistical representation of the sample set. Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) 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 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.