Question

The sum of the first

6

66 terms of a geometric series is

15

,

624

15,62415, comma, 624 and the common ratio is

5

55.

What is the first term of the series?

Answer 1

The first term of the series is 4

Explanation:

The sum of the first 6 terms of a geometric series is 15 , 624 and the common ratio is 5 .

To find the first term, we use the formula for the sum of terms in a geometric series.

Since the common ratio of the series is greater than 1, the sum of
`n^(th)` term of the geometric series is;

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

where r = common ratio

a = first term

When S = 15,624, r = 5 and n = 6, the first term, a, will be:

`15624 = (a(5^6 - 1))/(5 - 1) \\\\15624 = (a(15625 - 1))/(4)\\\\15624 = (a(15624))/(4)\\\\a = (4 * 15624)/(15624)`

a = 4

The first term of the series is 4.