Question

If the sum of first 10 natural numbers is $S_1$ and that of first 10 whole numbers is $S_2$ . Then $S_1-S_2$ is ___

• A. 20
• B. 10
• C. 30
• D. 40

Answer 1

The correct option is B

10

The set of natural numbers are (1,2,3,4,5...)
The set of whole numbers are (0,1,2,3...)

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

where $S_n$ is the sum of n terms of the AP,

'n' is the number of terms,

'a' is the first term,

'd' is the common difference.

$S_1=\frac{n}{2}(2a+(n-1\left)d\right)$

$S_1=\frac{10}{2}\left(2\right(1)+(10-1\left)1\right)=5(2+9)=55$

Similarly,

$S_2=\frac{10}{2}\left[2\right(0)+(10-1\left)1\right]$
$S_2=5\left(\right(2\times 0)+9)=45$
$\therefore$$S_1-S_2=55-45=10$