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# c2 geometric sequences question watch

1. cant seem to answer this question:

in a geometric progression, the second term is -4 and the sum to infinity is 9, find the common ratio?

i can see that a= -4/r and sum to infinity = a/1-r

the answer is -1/3 (teacher gave us the answers) but i cant get to that. any help would be appreciated
2. a = -4/r is correct

You also know the sum to infinity formula is a/1-r and you're told in the question that this equals 9

So you know a/(1-r) = 9

You have two equations and two unknowns, so what do you do?
3. What answer do you get? You have enough information to do the question; substitute into and solve for (it's probably easiest to multiply through by first).
4. How do you know r= -1/3 as opposed to 4/3?
5. (Original post by xHuStLeR23)
How do you know r= -1/3 as opposed to 4/3?
Because we need for the sum to infinity to converge.
6. Thanks for the help guys, had a bit of a blank and couldnt see that it was a quadratic giving r=4/3 and r=-1/3. i have no idea why it cant be 4/3, maybe my teacher made a mistake
7. (Original post by matt730)
i have no idea why it cant be 4/3
Work out the 10th, 100th and 1000th terms when it's -1/3, and again when it's 4/3, and you'll see why.
8. Work out the 10th, 100th and 1000th terms when it's -1/3, and again when it's 4/3, and you'll see why.
ahhh now it makes sense. Its been a long day of c2 revision lol

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