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# Core 2 - Geometric Progression

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1. Was wondering if anyone could help me out. I have the answers but one step i just can't get my head around.

In a geometric progression, the second term is -4 and the sum to infinity is 9. Find the common ratio.

I have:

ar = -4

a/1-r = 9

And then in the answers they jump from that to: -4/r = 9-9r
I just can't see why, and i'm probably being silly! Anyone help me out?
2. From the first equation: a = -4/r
From the second equation: a = 9(1-r) = 9-9r

So we have a= -4/r = 9-9r.
3. set both equations equal to 'a' then set them equal to each other then solve!!!

4. Thank you so much guys!

I see it now. *facepalm* I was being very thick.

Appreciate the help.
5. So what's the answer please? I ended up with two answers which can't be right (i guess I'm being thick seeing as this is last year's stuff)
6. you know the sum to infinity is 9 so if you sub in both of your answers only one will equal 9.. this is the correct answer

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