Question

Find the value of r for this geometric series

Answer 1

3

Explanation:

Pre-Solving

Recall that the formula for a term in a geometric sequence is
`t_n=t_1(r)^(n-1)`.

This formula in the sigma is the
`(2)/(9) (3)^(n-1)`.

Solving

As we can see, the 3 in
`(2)/(9) (3)^(n-1)` is in the place of where r is in
`t_1(r)^(n-1)`. So, this means that the value of r is 3.