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Question

For an A.P. a1,a2,...an and a1=52,a10=16.
If sum of n terms is 110 then n equals

A
9
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B
10
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C
11
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D
12
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Solution

The correct option is D 11
a1=52
Let the common difference be d.
Then
a10=a1+9d
16=52+9d
272=9d
d=32
Hence
Sn=n2(2(52)+(n1)32)
=n4(10+3(n1))
=n4(7+3n)
Now Sn=110
Hence
n4(7+3n)=110
n(7+3n)=440
3n2+7n440=0
n=11 and n=403
Since
n=403 is not possible, hence n=11

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