# Geometric Sequences and Series

1. Aug 21, 2011

### odolwa99

1. The problem statement, all variables and given/known data

Q.: The sum of the first five terms of a geometric series is 5 and the sum of the next five terms is 1215. Find the common ratio of this series.

2. Relevant equations

Sn = $\frac{a(r^n - 1)}{r - 1}$

3. The attempt at a solution

a + ar + ar^2 + ar^3 + ar^4 = 5
ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215

ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215
-(a + ar + ar^2 + ar^3 + ar^4) = 5
r^5 + r^5 + r^5 + r^5 + r^5 = 1210

5r^5 = 1210
r^5 = 242
r = $\sqrt[5]{242}$
r $\approx$ 3

Please note that $\sqrt[5]{243}$ is exactly 3. My answer is close but still off the mark. Can someone help me figure out how to fix this? Thank you.

2. Aug 21, 2011

### dynamicsolo

What if you factor r5 from your equation for 1215 and then divide it by the other equation? (Your approach is not algebraically correct.)

3. Aug 21, 2011

### odolwa99

Ok, here it is...

r^5(a + ar + ar^2 + ar^3 + ar^4) = 1215
a + ar + ar^2 + ar^3 ar^4 = 5

r^5 = $\frac{1215}{5}$

r^5 = 243
r = $\sqrt[5]{243}$
r = 3

That works out. Thank you very much.