Question

In an arithmetic progression, the $p^{th}$ term is $\frac{1}{q}$ and the $q^{th}$ term is $\frac{1}{p}$. Find the sum of the first ‘pq’ terms of the progression.

• A. pq + 1
• B.
• C.
• D. p*q

Answer 1

The correct option is B

Using Assumption

Let p = 1 and q= 2

Then as stated $1^{st}$ term is $\frac{1}{2}$ and $2^{nd}$ term is 1. So we have an AP with common difference$\frac{1}{2}$ .

So the AP is: $\frac{1}{2}$ , 1, $\frac{3}{2}$ , 2, $\frac{5}{2}$ ….

Now sum of first pq terms : sum of first two terms = $\frac{1}{2}$ + 1 = $\frac{3}{2}$

Put p = 1 and q = 2 in the options:

Correct option is (b)