Question

The sum of an infinite geometric series is 125, and the value of r is 0.4. How do you find the first three terms of the series?

Answer 1

The first three terms are `75, 30, 12`.

Explanation:

The formula for sum of an infinite, convergent geometric series is `s_oo = a/(1- r)`, where `s_oo` is the sum, `a` is the first term of the series and `r` is the common ratio.

Hence,

`125 = a/(1 - 0.4)`

`125 xx 0.6 = a`

`a = 75`

We know that `r = 0.4`, so:

`t_2 = 75 xx 0.4 = 30`

`t_3 = 30 xx 0.4 = 12`

Hopefully this helps!