Question

If p times the pth term of an A.P. is q times the qth term, then what is (p + q)th term equal to?

(a) p + q 

(b) pq 

(c) 1 

(d) 0

Answer 1

Answer : (d) 0

Given, p(a + (p – 1) d) = q (a + (q – 1)d), where a and d are the first term and common difference of the A.P. 

⇒ (p – q)a = (q² – q – p² + p)d 

⇒ – (q – p)a = (q – p) ((q + p) – 1) d 

⇒ – a = ((q + p) – 1)d 

⇒a + ((p + q) – 1)d = 0 

⇒ t_{p + q} = 0.