# Math

The third, fifth and seventeenth terms of an arithmetic progression are in geometric progression. Find the common ratio of the geometric progression.

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1. We can without loss of generality assume a=1, so

(1+4d)/(1+2d) = (1+16d)/(1+4d)
d = -5/8

The AP is 1, 3/8, -2/8, -7/8, -12/8, -17/8, -22/8, ... -9

The GP is 1, -5/8, 25/64, ...

(-12/8)/(-2/8) = 6
(-9)/(-12/8) = 6

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