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.


"a_1=2, a_2=5=a_1+3, a_3=9=a_2+4,"

"a_4=14=a_3+5,a_5=20=a_4+6,"

"a_6=27=a_5+7"

"a_n=a_{n-1}+n+1, n>1"

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

2.


"b_1=1, b_2=3=b_1(3), b_3=12=b_2(4),"

"b_4=60=b_3(5),b_5=360=b_4(6),"

"b_6=2520=b_5(7)"

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

"b_n=\\dfrac{(n+1)!}{2}, n\\geq1"





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