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Question
The fifth term of a G. P. is x, eighth term of the G. P. is y and eleventh term of the G. P. is z. Verify whether y2 = xz.
Solution
Given, t5 = x, t8 = y, t11 = z
Since, tn = arn–1
∴ t5 = ar4, t8 = ar7, t11 = ar10
Consider,
L.H.S. = y2 = (t8)2 = (ar7)2 = a2r14
R.H.S. = = xz = t5.t11 = ar4.ar10 = a2r14
∴ L.H.S. = R.H.S.
∴ y2 = xz.
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