If is the A.M. between a and b, then find the value of n.

Question

Philoid · Accepted Answer

A.M. of a and b =

Given, is the A.M. between a and b.

∴

⇒ (a + b) (a^n-1+ b^n-1) = 2aⁿ + 2bⁿ

⇒ aⁿ + ab^n-1 + ba^n-1 + bⁿ = 2aⁿ + 2bⁿ

⇒ ab^n-1 + ba^n-1 = aⁿ + bⁿ

⇒ ab^n-1 – bⁿ = aⁿ – ba^n-1

⇒ b^n-1 (a – b) = a^n-1 (a – b)

⇒

⇒ n – 1 = 0

∴ n = 1