Mathematics
The 5th, 8th and 11th terms of a G.P. are p, q and s respectively. Show that q2 = ps.
AP GP
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Answer
Let the first term of the G.P. be a and common ratio = r.
Given,
⇒ a5 = ar4 = p
⇒ a8 = ar7 = q
⇒ a11 = ar10 = s
We need to prove q2 = ps.
L.H.S. = q2
⇒ q2 = q × q = ar7 × ar7 = a2r14.
R.H.S. = ps
⇒ ps = p × s = ar4 × ar10 = a2r14.
∴ L.H.S. = R.H.S. = a2r14.
Hence, proved that q2 = ps.
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