Question

A geometric sequence is defined recursively by an = 4an-1. The 10th term of the sequence is a10 = 3.5. What is a13?

Answer 1

Using (I think) a different interpretation of the question than Spandy's answer (which I'm not certain I understand):
`color(white)("XXXX")` `a_13 = 224`

Explanation:

Assuming the "givens" are:
`color(white)("XXXX")` `a_n=4a_(n-1)`
`color(white)("XXXX")` `a_10 = 3.5`

`a_11 = 4*a_10 = 4*3.5 = 14`

`a_12 = 4*a_11 = 4*14 = 56`

`a_13 = 4*a_12 = 4*56 = 224`