Question

Write down the first five terms of the sequence an=(n+4)!2n2+6n+7a1 = a2 = a3 = a4 = a5 =

Answer 1

Step 1

Given;

`\begin{gathered} a_n=((n+4)!)/(2n^2+6n+7) \\ n=1,2,3,4,5 \end{gathered}`

Step 2

`a_1=((1+4)!)/(2(1)^2+6(1)+7)=(120)/(15)=8`
`a_2=((2+4)!)/(2(2)^2+6(2)+7)=(720)/(27)=(80)/(3)`
`a_3=((3+4)!)/(2(3)^2+6(3)+7)=(5040)/(43)`
`a_4=((4+4)!)/(2(4)^2+6(4)+7)=(8!)/(63)=640`
`a_5=((5+4)!)/(2(5)^2+6(5)+7)=(9!)/(87)=(120960)/(29)`