Question

Find the first five terms of the following sequence, starting with n=1. tn=(−1)n+1(n2−9) Give your answer as a list, separated by commas. For example, if tn=n, you would give your answer as 1,2,3,4,5.

Answer 1

-8, 5 , 0 , -7 , 16

Explanation:

Given

`t_n = (-1)^(n+1)(n^2 - 9)`

Required

The first five terms

When
`n = 1`

`t_1 = (-1)^(1+1)(1^2 - 9)`

`t_1 = (-1)^(2)(1 - 9)`

`t_1 = -8`

When
`n =2`

`t_2 = (-1)^(2+1)(2^2 - 9)`

`t_2 = (-1)^3 * (4 - 9)`

`t_2 = 5`

`t_3 = (-1)^(3+1)(3^2 - 9)`

`t_3 = (-1)^(4)(9 - 9)`

`t_3 = 0`

`t_4 = (-1)^(4+1)(4^2 - 9)`

`t_4 = (-1)^5(16 - 9)`

`t_4 = -7`

`t_5 = (-1)^(5+1)(5^2 - 9)`

`t_5 = (-1)^(6)(25 - 9)`

`t_5 = 16`

So, the first five terms are: -8, 5 , 0 , -7 , 16