Question

1. Write the first five terms of the sequence defined by the explicit formula an= (-2)^n-1. (1 point)

Answer 1

The first five terms of the sequence is 1, –2, 4, –8, 16.

Solution:

Given explicit formula is
`a_n=(-2)^(n-1)`.

To find the first five terms of the sequence, substitute n = 1, 2, 3, 4 and 5 in the given explicit formula.

For n = 1, we get

`a_1=(-2)^(1-1)`

`=(-2)^(0)`

= 1 (Using exponent rule
`a^0=1`)

For n = 2, we get

`a_2=(-2)^(2-1)`

`=(-2)^(1)`

`=-2`

For n = 3, we get

`a_3=(-2)^(3-1)`

`=(-2)^(2)`

= 4

For n = 4, we get

`a_4=(-2)^(4-1)`

`=(-2)^(3)`

= –8

For n = 5, we get

`a_5=(-2)^(5-1)`

`=(-2)^(4)`

= 16

Hence, the first five terms of the sequence is 1, –2, 4, –8, 16.