Mark the correct alternative in the following: 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

Question

Philoid · Accepted Answer

Here, S_p=q and S_q=p

i.e. and

i.e. ____(i)

and ____(ii)

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)

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

∴ 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

Now,

=-(p + q)