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Question
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
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Solution
Let the first term of the geometric progression = a
Common and ratio = r
5th term = ar5–1 = ar4 = p
8th term = ar8–1 = ar7 = q
11th term = ar11–1= ar10 = s
Left side = q2 = (ar7)2
= a2 × r14
Right side = ps = ar4 ar10
= a2 × r14
Hence, q2 = ps
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