Question

If a1,a2,a3, ......an are in HP, then a1a2 + a2a3 + .....+ an- 1an will be equal to

(A) a1an

(B) na1an

(C) (n - 1)a1 - an

(D) of these

Answer 1

Correct option (C) (n - 1)a1an

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

1/a2 - 1/a1 = 1/a3 - 1/a2 = ... = 1/an - 1/an - 1 = d

Adding these, we get

Also, nth term of this AP is given by

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