+1712 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!~
