The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.

Let a and r be the first term and common ratio respectively.

5th term = a5 = ar4
p = ar4

a8 = ar7

q = ar7

a11 = ar10

s = ar10

q2 = (ar7)2 = a2 r14

ps = ar4 ar10 = a2r4+10 = a2 r14

∴ q2 = ps

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