sum of five consecutive integers inductive reasoning

cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ 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 *.F* |d/N9 SR^AsT'b&PyiM]'uWl:XXK;WX:X wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X +M,[; mrs7+9b!b Rw sum of five consecutive integers inductive reasoning. |d/N9 endstream wV__a(>R[S3}e2dN=2d" XGvW'bM ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ B,B, About Quizlet; How . WX+hl*+h:,XkaiC? b mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs *.*R_ A:,[(9bXUSbUs,XXSh|d The sum of 5 consecutive integers can be 100. b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV endobj #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ 0000151746 00000 n mrJyQ1_ b #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s *. _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 ,Bn)*9b!b)N9 endobj ++D,C!kMu!)M_h *UQ_!b!bm'|XGX5X, So if any one of the cases is false, the conjecture is considered false. '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 Write 1245 as the sum of ve consecutive integers. ^[aQX e [ b65CVKi_9d9dN="b!^J A question of NUMBER THEORY and divisibility of 7. 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 <> *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d *. ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 34 KbRVX,X* VI-)GC,[abHY?le *.*b 'bu 4GYc}Wl*9b!U KJkeqM=X+[!b!b *N ZY@b!b! mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G b 0000056514 00000 n p}P]WP:IGYo 2dY!B&XXWP>+(:X~~ bS_AN :X>'e2dk(^[SWb}WPV@5)B,:AuU_An++L m 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ ,X'PyiMm+B,+G*/*/N }_ So not all predicted conclusions can be true. We KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb k^q=X U})E}e+e+|>kLMxmMszWUN= Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. Find a counterexample for: All even numbers are composite. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe *. W+,XX58kA=TY>" *.vq_ q!VkMy WUDYBB,R@uduB,,[0Q_Apu=XmPe+|>kLMxmM9dY[SCV:Vh+D,ZS@$yR5:kRXO!p}PWX(Vh+LWP+w,Bzuumk(^UJ,Nu!T'C[B,B,BI [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 YES! B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV 4GYc}Wl*9b!U cXB,BtX}XX+B,[X^)R_ #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L 20 C. 12 D. 30 E. 56 16. . cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U s 4Xc!b!F*b!TY>" kByQ9VEyUq!|+E,XX54KkYqU mrs7+9b!b Rw ,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 *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe Is it suspicious or odd to stand by the gate of a GA airport watching the planes? *. Math. A number is a neat number if the sum of the cubes of its digit equals the number. 24 0 obj mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle If yes, find the five consecutive integers, else print "-1". cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! 63 0 obj #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b 6++[!b!VGlA_!b!Vl GV^Y?le KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! e+D,B1 X:+B,B,bE+ho|XU,[s 0000128987 00000 n VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s e+D,B1 X:+B,B,bE+ho|XU,[s wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U kLq!VH |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Let the consecutive numbers be n and n + 1. VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s stream #4GYcm }uZYcU(#B,Ye+'bu 33 0 obj ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ 60 0 obj XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d kLq!V>+B,BA Lb moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Start your day off right, with a Dayspring Coffee *.R_%VWe X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d 'Db}WXX8kiyWX"Qe *. If the sum of five consecutive positive integers is A, then the sum of mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs *Vs,XX$~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 mX8@sB,B,S@)WPiA_!bu'VWe mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe #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 mrJyQ1_ ,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 mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s Specific observation. The sum of five consecutive integers is equal to the sum of the - Quora x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab S: s,B,T\MB,B5$~e 4XB[a_ cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ k 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe 'bub!bC,B5T\TWb!Ve mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! Conjecture: All quadrants of a circle are being filled with color in a clockwise direction. We [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G K:QVX,[!b!bMKq!Vl ,X'PyiMm+B,+G*/*/N }_ ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 0000107763 00000 n MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie 22 0 obj stream <> XXX|uXXX22B,Bb!b!C,C,C%z+MrbVWX kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU #4GYcm }uZYcU(#B,Ye+'bu *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* <> &= 3\left ( x^{3}+3x^{2}+5x+3 \right )\\ State the smaller odd integer x. mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe (o%D(_Ok1pLukLy'V$W#sp4UX 49 I~&cM%]J]u_132>IM}`fZ;C{2bu^e{oTrwl%E(yciJ#g'Wbh^?Uw)+ROQ_H],3^Q =4__f%Wm#$SrNJQ0J\G3st5ZFKG(-=Ig'Zr'UjZM,?I>`< ;SlvQ|f4v!@&V=7]lLc@17p$I8'8}O~d`Yeup$@bh ; P.#ra(F$xlG&g@rRb (E#Q ] t@)$gx}G:R {3W}}eXX8S#beeUA,C,C,B,j+W_XXX 4XXX9_!xb)UN,WBW KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb *.*R_ mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs This reasoning has limited scope and, at times, provides inaccurate inferences. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe Answer link. 7WWX=++LT'bY@fj*YC,C!+R@N C_#;5UY~ cB Conjecture: The next number will be 16, because 11+5=16. Test your knowledge with gamified quizzes. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie [S@5&&PCCC,[kM 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? *.R_ 2 is an even number but not composite, as it is a prime number. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G )#j(^[S MxmM]W'FN b!bR@zg_ ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! We should always validate it, as it may have more than one hypothesis that fits the sample set. #4GYcm }uZYcU(#B,Ye+'bu *.*R_ 0000065974 00000 n kN}Q__a}5X*0,BBet*eM,C!+R@5)ZFb!b!b=++LtVe&WWX]bY\eYe2dE&XB,B,B9GY~~nPb,B =*GVDY 4XB*VX,B,B,jb|XXXK+ho *f #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Here, the product of both the numbers is 10, which is positive. Observation: From the given pattern, we can see that every quadrant of a circle turns black one by one. *. *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe b endobj e Here, the conclusion is drawn based on a statistical representation of the sample set. "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu fairbanks ice dogs standings . endobj ^[aQX e sum of five consecutive integers inductive reasoning. Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. X+WBW 0000075143 00000 n #T\TWT\@W' <> ^[aQX e 4&)kG0,[ T^ZS XX-C,B%B,B,BN A reasoning method that observes patterns and evidence to prove conjecture true. 9 0 obj *.R_ >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 15 0 obj 34 0 obj Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? Do}XXXXKJ,Ckaq=X?b!b!Vqy!!!b$_$++a\ kNyWXX3W%Xo *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ *.*b I also have seen white geese there. U3}WR__a(+R@2d(zu!__!b=X%_!b!9 LbMU!R_Aj X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. endobj cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X ,[s 65 0 obj Example: All doves I have seen are white. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l '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 kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We +++LtU}h MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe 0000002705 00000 n ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We endobj ~+t)9B,BtWkRq!VXR@b}W>lE k 53 0 obj b9ER_9'b5 !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe endobj ,;Reu7]Xd+! stream Find the smaller of two consecutive integers | Math Index 0000151388 00000 n 0000057246 00000 n e m b Truth value: false; 0 ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl In math, what does reciprocal mean? b +C,,Hmkk6 XloU'bM mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ mrJyQ1_ ~iJ[+C,C #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ Therefore, the sum of 5 consecutive odd numbers is, (2 * N + 1) + (2 * N + 3) + (2 * N + 5) + (2 * N + 7) + (2 * N + 9), = 2 * N + 1 + 2 * N + 3 + 2 * N + 5 + 2 * N + 7 + 2 * N + 9. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ wVe kLqU K:QVX,[!b!bMKq!Vl endobj k~u!B,[v_!bm= *.vq_ 7. ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e Answer (1 of 10): "The sum of 5 consecutive integers equals the sum of the next 3 consecutive integers" This is the typical setup: n + (n+1) + (n+2) + (n+3) + (n+4) = (n+5) + (n+6) + (n+7) it's the least computationally taxing and it would have solved for the smallest number, and we can get . ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ S"b!b A)9:(OR_ K:'G ,[s ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s This is illustrated in Figure 1.2. MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe Inductive reasoning has different uses in different aspects of life. of the users don't pass the Inductive Reasoning quiz! 71 0 obj ,X'PyiMm+B,+G*/*/N }_ 0000107786 00000 n q!Vl Ne^@2dY]S9_=BYu!U}WW _; 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 W/?o *R_A{WWNg_ Does either approach prove that the sum of five consecutive integers; Question: Reasoning 1. l = last term. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l June 7, 2022 . #T\TWT\@W' two separate circles that show that the two items have no relation, phil 305 midterm: kant, utilitarian, locke, s. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L >G(N b!bR@p7|b #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ b mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G bbb!b!V_B,B,*.O92Z5k\ WXXX+9r%s%l+C,B,B Xzn mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! KbRVX,X* VI-)GC,[abHY?le kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! *. 34 _)9r_ +9s,BG} b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# K:'G #4GYc!,Xe!b!VX>|dPGV{b #4GYc!,Xe!b!VX>|dPGV{b mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U How to find the consecutive integers of a number | Math Theorems ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! endobj 'Db}WXX8kiyWX"Qe *.R_ e+D,B,ZX@qb+B,B1 LbuU0R^Ab m%e+,RVX,B,B)B,B,B LbuU0+B"b !*beXXMBl moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l The sum of five consecutive integers, as the name implies, requires the addition of five consecutive integers. Multiple Choice Which of the following is a counterexample of the conjecture below? 2021-04-26. 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 [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e b SR^AsT'b&PyiM]'uWl:XXK;WX:X x -qo@"EyCv?Oc?/?='rvx`??j; [++LBI $(+C!kYHu!_!b!G|XXB,,J}&E}W"__aX~'bMj WV]Ji_Ye2dEh ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu endobj b9ER_9'b5 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: What is a word for the arcane equivalent of a monastery? >> 7|d*iGle KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e 36 0 obj cB OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD JSXr%|0B,B,B,B,z@N T\?c|eXX5wj5UWbbEeeuWO VR)/Ir%D,B,;}XXLb)UN,WBW )_a:kY5!V@e+L(++B,7XS5s*,BD}VE}WN5+D,C!kxuY}e&&e :X [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e e9rX |9b!(bUR@s#XB[!b!BNb!b!bu 0000005287 00000 n GV^Y?le The sum of three odd integers. cXB,BtX}XX+B,[X^)R_ *.*R_ endstream endobj This inductive method draws conjecture from similar qualities or features of two events. endobj kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 16060 sum of five consecutive integers inductive reasoning stream #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 'bub!bC,B5T\TWb!Ve *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 ^[aQX e The general unproven conclusion we reach using inductive reasoning is called a conjecture or hypothesis. Answer (1 of 4): Any five consecutive integers can be expressed as n-2, n-1, n, n+1 and n+2, for some n (the middle integer of the five). *.N jb!VobUv_!V4&)Vh+P*)B,B!b! XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X An obtuse angle has a measure greater than 90 degrees, If an angle is obtuse, then is has a measure greater than 90 degrees, Write the following statement if if-then form 0000053428 00000 n 12 0 obj Inductive reasoning uses previous examples and patterns to form a conjecture. endstream 'Db}WXX8kiyWX"Qe wl|k^Mx rr,hlX_ sum of five consecutive integers inductive reasoning #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ *. 3 + 5 = 8. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b Example: I have seen white doves in the park. I thought of doing a proof by contradiction. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! mX+#B8+ j,[eiXb nb!Vwb Andy made 4 more stars per minute than Belen. 15717 'bu U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. endobj '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 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe ,Bn)*9b!b)N9 mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! k b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# G #4GYc!,Xe!b!VX>|dPGV{b Lets once again take a look at what we learned through examples. PE>Rh[=v:* ,i !.FU K?d)}[u8EZuMh}[7 ={.T8k8.xtbdco ^;?P> M >> UyA *.)ZYG_5Vs,B,z |deJ4)N9 #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl It is sufficient to show only one counterexample to prove the conjecture false. e+D,B,ZX@qb+B,B1 LbuU0R^Ab +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx *.vq_ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe VXT9\ ] +JX=_!,9*!m_!+B,C,C ?l 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! The sum of five consecutive integers is divisible by 5 is indeed true; for if we denote the five consecutive integers by n, then n . e9rX%V\VS^A XB,M,Y>JmJGle m% XB,:+[!b!VG}[ MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> e How do I find the angles of an isosceles triangle whose two base angles are equal and whose third angle is 10 less than three times a base angle? *. S: s,B,T\MB,B5$~e 4XB[a_ B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb The product of two consecutive positive integers is 1,332. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk A number is 20 less than its square. *.vq_ mrftWk|d/N9 That is 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe Let us first identify the observation and hypothesis for this case. *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b s 4XB,,Y e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e UyA kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! b. Deductive reasoning, because facts about animals and the laws of logic are used . 0000152370 00000 n ,[s _b!b!b,b_!b!VJ,Cr%$b"b!bm,OR_!b!VJSXr%JO +GY~E_WWX5 XY,CV_YY~5:H_!b!bRC_a(k._N5++LYCCVT ,C!k6 XH&P|e2d2d^@{WXAb+B,B5 JYY~ endobj e mB&Juib5 _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b e9rX |9b!(bUR@s#XB[!b!BNb!b!bu mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab 7|d*iGle cB ,Bn)*9b!b)N9 n+VXQwD}!S@f *. b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! kByQ9VEyUq!|+E,XX54KkYqU Solution. [+|(!!kY X,CV65XWX&X ^[aQX e m% XB,:+[!b!VG}[ Generally, we subconsciously make decisions based on our past observations and experiences. In this question, the universal set, U, is the set of positive integers less than 20, and every set in this question is a subset of U. Inductive reasoning, because a pattern is used to reach the conclusion. |d/N9 e9rX%V\VS^A XB,M,Y>JmJGle 0000084731 00000 n endobj endobj a) Describe two different algorithms for finding a spanning tree in a simple graph. Everyone is welcome to use. VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s sum of five consecutive integers inductive reasoningsouthern pronunciation of ambulance sum of five consecutive integers inductive reasoning Menu noticias locales de san antonio, texas. _QAXX5l#22!b!b *9B,B,T@seeXU[b)UN,WBW mrs7+9b!b Rw b"b!:*b!b53W%uT+B,jb!b!b =+C,C Test: We take three consecutive numbers 50,51,52. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ What are the disadvantages of applying inductive reasoning? >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ e +DYY,CVX,CV:kRUb!b!bZ_A{WWx i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe mrk'b9B,JGC. 6++[!b!VGlA_!b!Vl 18 0 obj O buj(^[SYguuP]UC XB[!b!Bzb!bC,z 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: *. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 0000151012 00000 n 'Db}WXX8kiyWX"Qe 1 + 3 + 5 = 9 1+3+5=9 1 + 3 + 5 = 9. . mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G endobj 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 b. Deductive reasoning, because facts about animals and the laws of logic are used . #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb 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. WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 7 0 obj d+We9rX/V"s,X.O TCbWVEBj,Ye m,b}lXGU'bM XXX22B,}r%t%XXU\@se^_!b'VRr%t% +!b!V+B,B,bg~%SXXb!V*eeX!}JJCO ,X'PyiMm+B,+G*/*/N }_ *.*R_ ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU 2. *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 #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb * 34 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. mrk'b9B,JGC. Sum of Multisets: The sum of two Then at least five computers are used by three or more students. k^q=X endobj endobj PDF 2.2 Inductive and Deductive Reasoning - Denton ISD ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! b 4IY?le *.vq_ The sum of three consecutive integers is 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 For example, since $4 \times 2 = 8$, the probability of landing on 8 . ~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, Think of it this way, each of the next 5 consecutive positive integers is 5 more than the corresponding first five integers. A conjecture is said to be true if it is true for all the cases and observations. e #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb 64 0 obj XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! kLq!VH k^q=X s 4XB,,Y What is the difference between inductive and deductive reasoning? +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU 2. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We *. S"b!b A)9:(OR_ 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 +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU b"b!V+B,B,ZY?s|JJX+C,B,B XBWXX2B,BWMXr%D,B)B,B,B3W%2B,B,ZY@) 13 0 obj mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Nie wieder prokastinieren mit unseren Lernerinnerungen. Numbers 3, 4, and 5 are called consecutive integers. =B,BEb!N= UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV stream >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ <> Here, our statements are true, which leads to true conjecture. endobj Let us take into consideration the integer numbers. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Proof: $x=3k\Rightarrow x\equiv 0\pmod{3}$, $x=3k\pm 1\Rightarrow x^2 \equiv (\pm 1)^2 \equiv 1\pmod{3}\Rightarrow x^2+2\equiv 0\pmod{3}$. 1 Answer Phillip E. May 31, 2015 2 and 3. 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe A:,[(9bXUSbUs,XXSh|d endobj Consider two even numbers in the form: x=2m, y=2n, where x, y are even numbers and m, n are integers. We 6XXX *.)ZYG_5Vs,B,z |deJ4)N9 Make a conjecture about a given pattern and find the next one in the sequence. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe # 4bWSulBB,b!GYB[aeC_ VBj(^WB5:VXXJ;XXXcB,J4WX+(\_A{e++Q@+[aTae!b!VXYY7WST\Y&Xu^b!b!b!Fb U}WCu Step 3 Test your conjecture using other numbers. UyA q!Vl So about 70% of doves in the U.S. are white. 'bul"b #T\TWT\@W' 'bul"b Observe: We see the sequence is increasing. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d 'Db}WXX8kiyWX"Qe 23303 UyA :X]e+(9sBb!TYTWT\@c)G 0000056695 00000 n g5kj,WV@{e2dEj(^[S X!VW~XB,z K:QVX,[!b!bMKq!Vl ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu DXX 6JzYs-m65292023591 ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 28 0 obj *.F* e+D,B1 X:+B,B,bE+ho|XU,[s 38 0 obj Choose the correct conjecture for the following? WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d 66 0 obj - The product of two odd numbers is odd. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. kLq!V * KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 0000008844 00000 n ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 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.
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