Question

The sum of the first 6 terms of a geometric series is

15, 624 and the common ratio is 5
What is the first term of the series?

Answer 1

4

Explanation:

The sum to n terms of a geometric sequence is

`S_(n)` =
`(a(r^n-1))/(r-1)`

where a is the first term and r the common ratio

Here r = 5 and a has to be found, thus

`S_(6)` =
`(a(5^6-1))/(5-1)`, so

`(a(15625-1))/(4)` = 15624

Multiply both sides by 4

15624a = 62496 ( divide both sides by 15624

a = 4