Question

In an A.P., if the p^th term is 'g' and the q^th term is 'p', then its n^th term is .....

(A) p + q - n

(B) p + q + n

(C) p - q + n

(D) p - q - n

Answer 1

The correct option is: (A) p + q - n

Explanation:

We have given that a_p = q and a_q = p

=> q = a+ (p - 1)d and      ....(i)

p = a + (q - 1)d       ....(ii)

Subtracting (ii) from (i), we get

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

Now, q = a + 1 - p         [From (i)]

=> a = q + p - 1

. ^.. a_n = a + (n - 1) d = q + p -1 +(n - 1) (- 1)

= q + p - 1 + 1 - n = q + p - n