Answer to Question #230866 in Calculus for Adnan Masood

Question #230866

Continue the two sequences of numbers below and find an equation to each of the sequences: n 1 2 3 4 5 6 7 Equation an 2 5 9 14 20 27 bn 1 3 12 60 360 2520

Please tell the complete solution of this question.


1
Expert's answer
2021-08-30T16:16:33-0400

1.


a1=2,a2=5=a1+3,a3=9=a2+4,a_1=2, a_2=5=a_1+3, a_3=9=a_2+4,

a4=14=a3+5,a5=20=a4+6,a_4=14=a_3+5,a_5=20=a_4+6,

a6=27=a5+7a_6=27=a_5+7

an=an1+n+1,n>1a_n=a_{n-1}+n+1, n>1

an=k=1n(k+1)=n(n+1)2+n=n(n+3)2,n1a_n=\displaystyle\sum_{k=1}^n(k+1)=\dfrac{n(n+1)}{2}+n=\dfrac{n(n+3)}{2}, n\geq1

2.


b1=1,b2=3=b1(3),b3=12=b2(4),b_1=1, b_2=3=b_1(3), b_3=12=b_2(4),

b4=60=b3(5),b5=360=b4(6),b_4=60=b_3(5),b_5=360=b_4(6),

b6=2520=b5(7)b_6=2520=b_5(7)

bn=bn1(n+1),n>1b_n=b_{n-1}(n+1), n>1

bn=(n+1)!2,n1b_n=\dfrac{(n+1)!}{2}, n\geq1





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