Question

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum or p + q terms will be 

A. 0 

B. p − q 

C. p + q 

D. − (p + q)

Answer 1

Option : (D)

Here, 

S_p = q and S_q = p

Now,

Multiplying (i) with q and (ii) with p and then subtracting we get 

pq(p-1)d - pq(q-1)d = 2q²-2p² 

∴pqd(p-q) = 2(q²-p²) 

∴ pqd(p-q) = 2(p-q)(p+q)

∴ d = \(-\frac{2(p+q)}{pq}\) 

Substituting the value of d in (i) we get,

2ap - \(\frac{p(p-1)2(p+q)}{pq}\) = 2q

∴ 2ap²q-2p(p-1)(p+q) = 2pq² 

∴ apq-(p-1)(p+q) = q² 

∴ apq = q²+(p-1)(p+q) 

∴ apq = q²+p²+pq-p-q