In an AP, the sum of the forst ten terms is -150 and the sum of it's next ten terms is -550. Find the AP
In an AP, the sum of the forst ten terms is -150 and the sum of it's next ten terms is -550. Find the AP
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ANSWER :-
S
10
=−150
S
n
=
2
n
[2a+(n−1)d]
S
10
=
2
10
[2a+(10−1)d]
−150=5(2a+9d)
∴−30=2a+9d...(1)
−550=
2
n
[2(a+10d)+(n−1)d]
−550=
2
10
[2(a+10d)+(10−1)d]
−550=
2
10
[2a+20d+9d]
−550=5[2a+29d]
−110=2a+29d...(2)
Solving (1) and (2) we get:
d=−4,a=3
Series: {3,−1,−5,−9,,,,,,,,,}