Question

Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.

n an
1 −4
2 20
3 −100

an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4

Answer 1

Given:

The geometric sequence is:

`n`
`a_n`

1 -4

2 20

3 -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

`a_n=ar^(n-1)` ...(i)

Where, a is the first term, r is the common ratio and
`n\geq 1`.

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

`r=(a_2)/(a_1)`

`r=(20)/(-4)`

`r=-5`

Putting
`a=-4,r=-5` in (i), we get

`a_n=-4(-5)^(n-1)` where
`n\geq 1`

Therefore, the correct option is B.