NIMCET 2013 Question Paper with solutions

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Question : 22 of 120

Marks: +1, -0

The sum of n terms of an arithmetic series is 216. The value of the first term is n and the value of the nth term is 2n The common difference, d is:

1
2/3
3/2
12/11

Solution:

∵S_n=216

∵n/2[2a+(n-1)d]=216

where,

T_n=2n

a=n

2n=n+(n-1)d

n=(n-1)d

and

d=n/(n-1)

∴n/2[2n+(n-1)×n/(n-1)]=216

⇒n/2[3n]=216⇒{3n^2}/2=216

⇒n^2={216×2}/3=72×2

⇒n^2=144⇒n=12

∴d=12/11

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