the sum of the first 6 terns of an AP is 36 and that of the first 16 terms is 256 .Find the sum of first 11 terms.
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We have the sum of first n terms of an AP,
S
n
=
2
n
[2a+(n−1)d]
Given,
36=
2
6
[2a+(6−1)d]
12=2a+5d ---------(1)
256=
2
16
[2a+(16−1)d]
32=2a+15d ---------(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S
10
=
2
10
[2(1)+(10−1)2]
S
10
=5[2+18]
S
10
=100
This is the sum of the first 10 terms
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