# Thread: geometric series

1. ## geometric series

Hi all
Theres this question about a geometric series that i can't figure out.
It says the second term is 375 and the fifth term is 81 and you have to show that the common ratio of the series is 0.6
I can't get the right answer :S

Thanks for the help x

2. Use the normal geometric progression and substitute the values you have

Term 2 = 375;
Term 5 = 81;

SO now you have to simultaneous equations

Can be solved

3. Originally Posted by katiethegreat
Hi all
Theres this question about a geometric series that i can't figure out.
It says the second term is 375 and the fifth term is 81 and you have to show that the common ratio of the series is 0.6
I can't get the right answer :S

Thanks for the help x
you should know the form of a geometric series ...

$\displaystyle a + ar + ar^2 + ar^3 + ...$

2nd term ...

$\displaystyle ar = 375$

5th term ...

$\displaystyle ar^4 = 81$

divide the 5th term by the 2nd term ...

$\displaystyle \frac{ar^4}{ar} = \frac{81}{375}$

$\displaystyle r^3 = \frac{27}{125}$

$\displaystyle r = \frac{3}{5}$