Question

The sum of an infinite geometric series is 81, and its common ratio is 2/3, how do you find the first three terms of the series?

Answer 1

`a_1 = 27, a_2 = 18, a_3 = 12`

Explanation:

We use the formula `s_oo = a/(1 - r)` to find the sum of an infinite geometric series, where `-1 < r < 1`. We know the sum and the common ratio, so we'll be solving for `a`.

`s_oo = a/(1 - r)`

`81 = a/(1 - 2/3)`

`81 = a/(1/3)`

`81 = 3a`

`a = 27`

Since our common ratio is `2/3`, we multiply the first term by a factor of `2/3` to get our second term, and our second term by `2/3` to get our third term.

Hence,

`a_2 = 18`
`a_3 = 12`

Hopefully this helps!