Here, a, b, c are in G.P.⇒ b2 = ac⇒ (b2)n = (ac)n⇒ b2n = ancn Taking log on both sides, we getlog (b2n) = log (ancn)⇒ log(bn)2 = log an + log cn⇒ 2log bn = log an + log cn⇒ log bn + log bn = log an + log cn⇒ log bn - log an = log cn - log bn⇒ log an, log bn and log cn are in A.P.

English

Q 1.2 -

Question

Q 1.2

Sum

Solution

Here, a, b, c are in G.P.
⇒ b² = ac
⇒ (b²)ⁿ = (ac)ⁿ
⇒ b²ⁿ = aⁿcⁿ

Taking log on both sides, we get
log (b²ⁿ) = log (aⁿcⁿ)
⇒ log(bⁿ)² = log aⁿ + log cⁿ
⇒ 2log bⁿ = log aⁿ + log cⁿ
⇒ log bⁿ + log bⁿ = log aⁿ + log cⁿ
⇒ log bⁿ - log aⁿ = log cⁿ - log bⁿ
⇒ log aⁿ, log bⁿ and log cⁿ are in A.P.