Question

The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?

Answer 1

`a_n=5a_(n-1)`

Explanation:

Given fifth term of a geometric sequence is 781.25.

`a_5= 781.25`.

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

`a_n=ra_(n-1)`

Plugging value of r in above formula, we get

`a_n=5a_(n-1)`

Therefore, recursive formula would be
`a_n=5a_(n-1)` represents the situation.