I was just doing random math problems-like you do, and I stumbled upon this one...

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?

WORK/ATTEMPT:

Okay, so I'll start by saying what I already know.

The common ratio is the amount between each number in a geometric sequence.

The sum is the sum...

The formula for the sum of a finite geo series:

\(S_n=a_1(\frac{1-r^n}{1-r})\)

And our given is:

\(S_n=15624 \\n=6 \\r=5\)

So when we plug it in:

\(=15,624 = a_{1} (\frac{1 - 5^{6}}{1 - 5})\)

\(=15,624 = a_{1} (\frac{-15,624}{-4})\)

\(=15,624 = a_1 (3,906)\)

\(a_1 = 4\)

So I'm just checking if four is my right answer...

Thanks!~

tommarvoloriddle Jan 2, 2020