Question

For what value of n a(n+1)+b(n+1)/a(n)+b(n) is the A.p of the number a and b.

Answer 1

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•Answer:-

• n = 0

•Step-by-step explanation:-

(aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) is mean between a & b

Mean of a & b =  ( a + b)/2

=> (aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) = ( a + b)/2

=> 2aⁿ⁺¹ + 2bⁿ⁺¹  = aⁿ⁺¹  + bⁿ⁺¹  + baⁿ + bⁿa

=> aⁿ⁺¹ + bⁿ⁺¹ = baⁿ + bⁿa

=> aⁿ(a - b) = bⁿ(a - b)

=> aⁿ = bⁿ

=> (a/b)ⁿ = 1

=> n = 0    or a  = b