If the sum of p terms of an AP is g and the sum ofg terms is p, then the sum.
of p + q terms will be.
(a) 0
(b) p-9
(c) p +9
(d) - (p +9)
Answers
Answered by
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]
=
2
p+q
×[2a+(p−1)d+qd]
=
2
p+q
×[
p
2q
+q(
qp
−2(q+p)
)]
=
2
p+q
×(
p
2q−2q−2p
)
=−(p+q)
Step-by-step explanation:
HOPE THIS HELPS YOU.
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