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Question
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2 = pr.
Solution
Let the first term of the G.P. be a and its common ratio be r.
5th term = t5 = p
`=>` ar4 = p
8th term = t8 = q
`=>` ar7 = q
11th term = t11 = r
`=>` ar10 = r
Now,
pr = ar4 × ar10
= a2 × r14
= (a × r7)2
= q2
`=>` q2 = pr
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