Question

If a₁,a₂,a₃, ......a_n are in HP, then a₁a₂ + a₂a₃ + .....+ a_{n - 1}a_n will be equal to

(A)  a₁a_n

(B)  na₁a_n

(C)  (n - 1)a₁ - a_n

(D)  None of these

Answer 1

Correct option  (C) (n - 1)a₁a_n

Since a₁,a₂,a₃, ......a_n are in HP, therefore 1/a₁,1/a₂,1/a₃ .....1/a_n will be in AP Which gives

1/a₂ - 1/a₁ = 1/a₃ - 1/a₂ = ... = 1/a_n - 1/a_{n - 1} = d

Adding these, we get

Also, n^th term of this AP is given by

Now substituting this value of d in Eq. (1). We get