Asked by Gustav
The third, fifth and seventeenth terms of an arithmetic progression are in geometric progression. Find the common ratio of the geometric progression.
Answers
Answered by
Steve
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
(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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