Question

The sum of first 50 odd natural numbers is __________.

Answer 1

First 50 odd natural numbers are: 1, 3, 5, 7, ...

First term (a) = 1
Common difference (d) = 3 – 1 = 2

Now,
$$\begin{gathered} S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right] \\ {S}_{50}=\frac{50}{2}\left[2a+\left(50-1\right)d\right] \\ =25\left[2\left(1\right)+49\left(2\right)\right] \\ =25\left[2+98\right] \\ =25\times 100 \\ =2500 \end{gathered}$$

Hence, the sum of first 50 odd natural numbers is 2500.