Infinity geometric series question

[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?

 

[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?

 

[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

 

[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.