Q. 154.2( 115 Votes )

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

Answer :

A.M. of a and b =

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

∴

⇒ (a + b) (a^{n-1}+ b^{n-1}) = 2a^{n} + 2b^{n}

⇒ a^{n} + ab^{n-1} + ba^{n-1} + b^{n} = 2a^{n} + 2b^{n}

⇒ ab^{n-1} + ba^{n-1} = a^{n} + b^{n}

⇒ ab^{n-1} – b^{n} = a^{n} – ba^{n-1}

⇒ b^{n-1} (a – b) = a^{n-1} (a – b)

⇒

⇒

⇒ n – 1 = 0

∴ n = 1

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