Question

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

Answer 1

A is the answer for this question

Answer 2

Option A.
`a_(n)=(-7)((1)/(3) )^(n-1)`

Explanation:

Recursive formula of the geometric sequence is given as
`a_(1)=(-7)`

and
`a_(n)=(1)/(3)(a_(n-1))`

From these formulas it is clear that first term of the sequence a1 = -7

and common ratio of the sequence =
`(1)/(3)`

Since explicit formula of any geometric sequence is represented by

`a_(n)=a_(1)(r)^(n-1)`

Therefore,
`a_(n)=(-7)((1)/(3) )^(n-1)` will be the explicit formula of the given geometric sequence.