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

Answer 1

The correct option is A 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

$\to$pd – d – qd + d = q – p

$\to$d (p – q) = q – p

$\to$ d = -1

a = q – (p – 1)d = q + (p – 1)

So, $m^{th}$ term = q + p – 1 – (m – 1) = q + p – 1-m + 1 = p + q – m