## If the pth term of an AP is q and the qth term is p, prove that its nth term is (p+q-n).

A. Twice of pth term

B. 2(p + q)

C. (p + q – n)

D. None of these

### Answer

Correct Answer: **C. (p+q-n)**

### Solution

Given pth term is q and qth term is p.

a_{p} => a+(p-1)d = q…(i)

a_{q} => a+(q-1)d =p …(ii)

(i) – (ii)

(p-1-q+1) d = q-p

(p-q) d = (q-p)

d = -1

Substitute d in (i)

a-p+1 = q

a = p+q-1

rth term = a+(n-1)d

= p+q-1-(n-1)

= p+q-n

Hence option (2) is the answer.