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Question
The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz
Solution
Let a be the first term and r be the common ratio of the G.P.
Then t5 = x, t8 = y and t11 = z
Using tn = arn–1, we get
ar5–1 = x, ar8–1 = y and ar11–1 = z
∴ ar4 = x, ar7 = y and ar10 = z
∴ y2 = (ar7)2 = a2r14
= (ar4)(ar10) = xz
Hence, y2 = xz
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