S(p)=q,S(q)=p then find S(p+q)
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Answered by
1
Sp = q, sq = p, find S
p+q
=?
First term = a, Common difference = d
S
p
=
2
P
[2a+(p−1)d]=q...(1)
S
q
=
2
q
[2a+(q−1)d]=p...(2)
S
p+q
=
2
p+q
[2a+(p+q−1)d]
2ap+p(p−1)d=2q×q
2aq+q(q−1)d=2p×p
⇒2apq+pq(p−1)d=2q
2
2apq+qp(q−1)d=2p
2
_____________________
pqd(p−1−q+1)=2(q
2
−p
2
)
⇒qpd=−2(p+q)
d=
pq
−2(p+q)
...(3)
S
p+q
=
2
p+q
[2a+(p+q−1)d]
=
2
p+q
[2a+(p−1)d]+
2
(p+q)
qd
S
p+q
=
2
p+q
×
p
2q
+
2
(p+q)q
×
qp
−2(p+q)
S
p+q
=
p
(p+q)
(q−p−q)
S
p+q
=−(p+q)
So, option (B) is correct.
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