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How do you find the common ratio in a geometric progression when the sum of the first 20 terms is 244 times the sum of its first 10 terms?
Sum of 10 terms is n(r10-1)/(r-1) where n = 1st term. Sum of 20 is n(r20-1)/(r-1) so ratio is (r20-1)/(r10-1). Let r10 be called x. So the ratio is (x2-1)/(x-1) which is just x+1, so x=243. The common ratio is therefore the 10th root of this. Which is square root of 3.
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