Question

If the sum of first p terms of an AP is q and the sum of first q terms is p, then find the sum of first (p +q)
terms.​

Answer 1

Answer:

S

p

=

2

p

×[2a+(p−1)d]=q........(i)

S

q

=

2

q

×[2a+(q−1)d]=p........(ii)

S

p+q

=

2

p+q

×[2a+(p+q−1)d]

From equation (i) and (ii), we get,

2

p

×[2a+(p−1)d]=q

=>2a+(p−1)d=

p

2q

........(iii)

and

2

q

×[2a+(q−1)d]=p

=>2a+(q−1)d=

q

2p

........(iv)

Subtracting (iii) and (iv), we get,

q

2p

−

p

2q

=(q−p)d

=>

pq

2(p+q)(p−q)

=(q−p)d

=>d=

pq

−2(p+q)

........(v)

Now, S

p+q

=

2

p+q

×[2a+(p+q−1)d]