# Infinity geometric series question

1. Jun 14, 2006

### Emma O'shea

Hi there everyone!
Have a quick question for you.
The question is:
The sum to infinity of a geometric series is 9/2
The second term of the series is -2
Find the value of r, the common ratio of the series.

I understand that we have to use the sum to infinity of a geometric series formula which is S(infinity) = a/1-r

where a is the first term in the series and r is the common ratio.
I also understand that s2 = s1*r.

We're given the second term....but how do we get a? our first term?
Any thoughts?

2. Jun 14, 2006

### matt grime

if you understand the second term is r times the first term, then you understand the first time is what times the second term?

3. Jun 14, 2006

### Emma O'shea

The first term is the second term over r.
Well spotted!!
I'll get the hang of this stuff yet!!

Thanks very much

4. Jun 14, 2006

### HallsofIvy

So you now know that a= -2/r and that
$$\frac{a}{1-r}= \frac{-2}{r(1-r)}= 9/2$$
Solve for r.

Last edited by a moderator: Jun 15, 2006
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook