Question

What is the explicit formula for the geometric sequence with this recursive formula?

Answer 1

A

Explanation:

The explicit formula for a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

The recursive formula gives a term in the sequence by multiplying the previous term by r

Given the recursive formula

a₁ = - 6

`a_(n)` =
`a_(n-1)` (
`(1)/(4)` )

with r =
`(1)/(4)`

Then explicit formula is

`a_(n)` = - 6
`((1)/(4)) ^(n-1)` → A