Question

If the p^th term of an AP is q and its q^th term is p, then what will be the value of its (p + q)^th term?

(a) 1

(b) p + q – 1

(c) 0

(d) 2(p + q – 1)

The question was posed to me during an online exam.

Origin of the question is Nth Term of Arithmetic Progression in chapter Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right choice is (c) 0

Easiest explanation: p^th term = q

a + (p – 1)d = q

a + pd – d = q     (1)

q^th term = p

a + (q – 1)d = p

a + qd – d = p     (2)

Subtracting (2) from (1) we get,

a + qd – d – (a + pd – d) = p – q

qd – pd = p – q

d = -1

Substituting in equation 1, we get,

a = p + q – 1

(p + q)^th term = a + (n – 1)d = p + q – 1 + (p + q – 1)(-1) = p + q – 1 – p – q + 1 = 0