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Sets and Integers | TOMATO B.Stat Objective 121

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Sets and Integers. You may use sequential hints.

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Sets and Integers.

Sets and Integers ( B.Stat Objective Question )


For each positive integer n consider the set \(S_n\) defined as follows \(S_1\)={1}, \(S_2\)={2,3}, \(S_3\)={4,5,6}, …, and , in general, \(S_{n+1}\) consists of n+1 consecutive integers the smallest of which is one more than the largest integer in \(S_{n}\). Then the sum of all the integers in \(S_{21}\) equals

  • 1113
  • 4641
  • 53361
  • 5082

Key Concepts


Sets

Integers

Sum

Check the Answer


But try the problem first…

Answer: 4641.

Source
Suggested Reading

B.Stat Objective Problem 121

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

\(S_1\) has 1 element

\(S_2\) has 2 element

…..

\(S_{20}\) has 20 element

Second Hint

So number of numbers covered=1+2+3+…+20

sum =\(\frac{(20)(21)}{2}\)=210

\(S_{21}\) has 21 elements with first element= 211

Final Step

sum of n terms of a.p series with common difference d,

\(sum=\frac{n}{2}[2a+(n-1)d]\)

Then in our given question no of terms n=21 and c.d =1

Then the sum of elements=\(\frac{21}{2}[(2)(211)+(20)(1)]\)=4641.

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