Question

Find the sum of the first 20 natural numbers. Choose the correct option:
A. 210
B. 220
C. 230
D. 240

Answer 1

Hint: It is known that the natural number starts from 1. Also, the sum of the first n natural number is given by: $${\displaystyle \frac{n(n+1)}{2}}$$.

Complete step-by-step answer:
In the given problem, we have to find the sum of the first 20 natural numbers.
Now the natural number always starts from 1 and that means 1 is the smallest natural number.
Next, the first 20 natural number will be:
1, 2, 3, 4, 5, …….., 19, 20. Here there are 20 terms.

Now we know that the sum of the first n natural number is given by the formula $${\displaystyle \frac{n(n+1)}{2}}$$.
Also, n here is the number of terms and that is equal to 20.
$$\Rightarrow n=20$$
So the sum of first 20 natural number will be given:
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{n(n+1)}{2}}\\ & \Rightarrow {\displaystyle \frac{20(20+1)}{2}}\\ & \Rightarrow 10(21)\\ & \Rightarrow 210\end{array}$$
So, now the correct option is A) 210.

Note: It is important to keep in mind that zero is not the natural number. Also, the smallest natural number is one. This problem can also be solved by using the sum of n terms of an arithmetic progression formula i.e. $S_n={\displaystyle \frac{n}{2}}[2a+(n-1)d]$ where first term (a) = 1, common difference (d) =1 and n =20.