Question

Find the value of a^4 for this geometric series

Answer 1

a₄ = 6

Explanation:

the nth term of a geometric series is

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

where a₁ is the first term and r the common ratio

the expression inside the ∑ is in this form, that is

`a_(n)` =
`(2)/(9)`
`(3)^(n-1)`

with a₁ =
`(2)/(9)` and r = 3 , then

a₄ =
`(2)/(9)`
`(3)^(4-1)` =
`(2)/(9)` × 3³ =
`(2)/(9)` × 27 = 2 × 3 = 6