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Tricky geometric series question

Hi. I just completed a C2 mock today, and I thought I was pretty confident in geometric series...until I got this question. (not exact, I'm paraphrasing)

The sum of the first 2 terms in a geometric series with all positive terms is 32 and the sum to infinity is 164.
I) Find the common ratio
II) Find the first term.

The second part I know how to do, IF I could figure out the common ration. The problem is I keep getting weird equations like r-1=32a and a=162-162.

Any help would be appreciated, thanks.
We know:
[br]S2=32=a(1−r2)1−r[br][br]S_2 = 32 = \frac{a(1-r^2)}{1-r}[br]

and
[br]S∞=164=a1−r[br][br]S_\infty = 164 = \frac{a}{1-r}[br]

Then by some rearranging:
[br]32(1−r)=a(1+r)(1−r)[br][br]32(1-r) = a(1 + r)(1 - r)[br]
[br]a=32(1−r)(1+r)(1−r)[br][br]a= \frac{32(1-r)}{(1+r)(1-r)} [br]
[br]a=321−r[br][br]a= \frac{32}{1-r}[br]

and

[br]164(1−r)=a[br][br]164(1-r) = a[br]

Equate those two to each other and you should find r :h:

(I think some of these equations might not render properly; sorry, I don't really know TSR-specific Latex formatting!

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