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 D11 a1=52 Let the common difference be d. Then a10=a1+9d 16=52+9d 272=9d d=32 Hence Sn=n2(2(52)+(n−1)32) =n4(10+3(n−1)) =n4(7+3n) Now Sn=110 Hence n4(7+3n)=110 n(7+3n)=440 3n2+7n−440=0 n=11 and n=−403 Since n=−403 is not possible, hence n=11