+0  
 
+1
119
1
avatar+1694 

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
avatar+16 
+1

Yes, It's correct!

 Jan 2, 2020

24 Online Users

avatar
avatar
avatar