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

Staff Emeritus
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: Jun 15, 2006