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Question

The sets S1,S2,S3..... are given by S1=21,S2=32,52,S3=43,73,103,S4=54,94,134,174........ Then the sum of the numbers in set S25 is


A

320

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B

322

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C

324

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D

326

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Solution

The correct option is D

326


Explanation for correct option:

S1=2,1S2=32,52S3=43,73,103S4=54,94,134,174

The sequence in the sets is Sn=1+1n,2+1n,3+1n,......nterms

Which is an arithmetic progression with the first term being 1+1n and common difference d=1

So,S25=1+125,2+125,........25terms

Sum of all elements in S25=sum of the arithmetic progression

Sum of arithmetic progression=n22a+(n-1)d

For S25, n=25

Sum of all elements in S25=25221+125+(25-1)1

⇒S25=2522×2625+24⇒S25=2525225+24⇒S25=25265225⇒S25=326

Hence, option D is correct.


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