# Thread: find the value of a in this sequence

1. ## find the value of a in this sequence

a, 3a,...
The first term in the sequence above is a, and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605, what is the value of a? I got 25 but the correct answer is 5. Why? THanks in advance

2. Originally Posted by fabxx
a, 3a,...
The first term in the sequence above is a, and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605, what is the value of a? I got 25 but the correct answer is 5. Why? THanks in advance
So I guess you weren't far from the solution.
It would be nice if you showed it after that, so that one can tell you what was wrong.

$a+3a+3^2a+3^3a+3^4a=605$

This can be factored : $a(1+3+3^2+3^3+3^4)=605$

What's in brackets is a geometric sum. We know that $1+r+r^2+\dots+r^{n-1}=\frac{1-r^n}{1-r}$

Can you do it ?