if the sum of P term of an AP is the same as the sum of its q term, show that the sum of its (P+q) term is zero.
Answers
Answered by
0
Step-by-step explanation:
ANSWER
S
p
=S
q
⇒
2
p
(2a+(p−1)d)=
2
q
(2a+(q−1)d)
⇒ p(2a+(p−1)d)=q(2a+(q−1)d)
⇒ 2ap+p
2
d−pd=2aq+q
2
d−qd
⇒ 2a(p−q)+(p+q)(p−q)d−d(p−q)=0
⇒ (p−q)[2a+(p+q)d−d]=0
⇒ 2a+(p+q)d−d=0
⇒ 2a+((p+q)−1)d=0
⇒ S
p+q
=0
Answered by
3
Step-by-step explanation:
ANSWER
S
p
=S
q
⇒
2
p
(2a+(p−1)d)=
2
q
(2a+(q−1)d)
⇒ p(2a+(p−1)d)=q(2a+(q−1)d)
⇒ 2ap+p
2
d−pd=2aq+q
2
d−qd
⇒ 2a(p−q)+(p+q)(p−q)d−d(p−q)=0
⇒ (p−q)[2a+(p+q)d−d]=0
⇒ 2a+(p+q)d−d=0
⇒ 2a+((p+q)−1)d=0
⇒ S
p+q
=0
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