il the sum of first 7 terms of an AP is 49 and that of 17 terms is 289. find the sum of first n terms of the AP.
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Answered by
0
Step-by-step explanation:
ANSWER
Given
S
7
=49 and S
17
=289
By using S
n
=
2
n
[2a+(n−1)d] we have,
S
7
=
2
7
[2a+(7−1)d]=49
⇒49=
2
7
[2a+(7−1)d]
⇒49=
2
7
(2a+6d)
⇒7=a+3d
⇒a+3d=7...................(i)
S
17
=
2
17
[2a+(17−1)d]=289
⇒289=
2
17
[2a+(17−1)d]
⇒289=
2
17
(2a+16d)
⇒17=a+8d
⇒a+8d=17......................(ii)
Substituting (i) from (ii), we get
5d=10 or d=2
From equation (i),
a+3(2)=7
a+6=7 or a=1
S
n
=
2
n
[2(1)+(n−1)2]
=
2
n
[2+(n−1)2]
=
2
n
(2+2n−2)=n
2
Answered By ABHINAVROCKS
Answered by
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