Question

Extending the same logic you’ve seen in the video so far, find out the sum of the first 10 natural numbers
(Consider $S_{10}=1+2+3+\dots +10$ to proceed.).

• A. 110
• B. 55
• C. 220
  
• D. 66

Answer 1

The correct option is B 55

Let $S_{10}$ denote the sum of first 10 natural numbers.
$\therefore S_{10}=1+2+3+4+5+6+7+8+9+10---\left(1\right)$
Since reversing the order in which the numbers are added will not change the sum, we have
$S_{10}=10+9+8+7+6+5+4+3+2+1.---\left(2\right)$
Adding equations (1) and (2), we have
$2S_{10}=11+11+11+11+11+11+11+11+11+11.$
$2S_{10}=11\times 10$
$\Rightarrow S_{10}=\frac{11\times 10}{2}=55$
Thus, the sum of first 10 natural numbers is 55.