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# Hi!!! I'm Back~

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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!~

Jan 2, 2020

### 1+0 Answers

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Yes, It's correct!

Jan 2, 2020