Question

The sum of first 20 terms of an AP is 400 and the sum of its first 40 terms is 1600.Find the sum of its first 10 terms.

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Answer 1

Sn=n/2(2a+(n-1)d)

=>S20=10(2a+19d)=400

=>2a+19d=40------(1)
......
Similarly,
S40=20(2a+39d)=1600

=>2a+39d=80-------(2)

By solving (1) and (2),

=>-20d=-40

Hence,d=2.

(1)=>2a+19(2)=40

=>2a+38=40

=>2a=2

Hence, a=1.

Therefore,
S10=10/2(2+9(2))

=5(20)

=100.
.....
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Answer 2

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