If 5th, 8th and 11th terms of a G.P. are p, q and s respectively, prove that a2 = ps.
Tn = arn-1
According to the question,
⇒ T5 = a.r4
⇒ T8 = a.r7
⇒ T11 = a.r10
To Prove: q2=p.s
⇒ T5 = a.r4 = p
⇒ T8 = a.r7 = q
⇒ T11 = a.r10=s
q2= (a.r7)2 = a2.r14…(1)
p.s = (a.r4)(a.r10) = a2.r14…(2)
∴ from (1) and (2) we get
⇒ q2=p.s
Hence, Proved.