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# Tricky geometric series question

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1. 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.
2. We know:

and

Then by some rearranging:

and

Equate those two to each other and you should find r

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

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