# Sets and Integers | TOMATO B.Stat Objective 121

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

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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