If in an A.P., the pᵗʰ term is q and the (p + q)ᵗʰ term is 0, then the qᵗʰ term is:

Correct option is B

Given:

pᵗʰ term = q
(p + q)ᵗʰ term = 0

Concept used:
nᵗʰ term of an A.P.:
Tₙ = a + (n − 1)d

Solution:
Tₚ = a + (p − 1)d = q ...(1)
T₍ₚ₊q₎ = a + (p + q − 1)d = 0 ...(2)

Subtract (1) from (2):
[a + (p + q − 1)d] − [a + (p − 1)d] = 0 − q
=> qd = −q
=> d = −1

Substitute in (1):
a + (p − 1)(−1) = q
=> a − p + 1 = q
=> a = q + p − 1

Now find qᵗʰ term:
T_q = a + (q − 1)d
= (q + p − 1) + (q − 1)(−1)
= q + p − 1 − q + 1
= p

Correct answer is (b) p.