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.
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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]
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