Mathematics
The fifth, eighth and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2 = pr.
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Answer
Let first term of the G.P. be A and it's common ratio be R.
Given,
⇒ a5 = p
⇒ AR4 = p ……..(i)
Also,
⇒ a8 = q
⇒ AR7 = q ………(ii)
⇒ a11 = r
⇒ AR10 = r ………(iii)
Multiplying (i) by (iii) we get,
AR4 x AR10 = pr
⇒ A2R14 = pr ………(iv)
Squaring eq. (ii) we get,
(AR7)2 = q2
A2R14 = q2 ………(v)
L.H.S. of eq. (iv) and (v) are equal so, R.H.S. will also be equal.
∴ q2 = pr.
Hence, proved that q2 = pr.
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