Question

If the p_th term of an AP is q and its q_th term is p then its m_th term is:

• A. pq/m
• B. p + q – m
• C. p + q + m
• D. pq + m
• E. pqm

Answer 1

The correct option is B p + q – m

p_th term = a + (p – 1) d = q ... (i)

q _th term = a + (q – 1) d = p ... (ii)

Subtracting (ii) from (i)

(p – 1) d – (q – 1) d = q – p

->pd – d – qd + d = q – p

->d (p – q) = q – p

-> d = -1a = q – (p – 1)d = q + (p – 1)

So, m_th term = q + p – 1 – (m – 1) = q + p – 1-m + 1 = p + q – m

Hence option (b)

Alternatively, use assumption

Let the first term=2 and the 2^nd term=1, therefore p=1 and q=2

Let m=3

Thus, 3^rd term=0. Substitute the values of p,q and m in the answer options and look for 0. Only option (b) gives this value