Questions & Answers

Question

Answers

A. 210

B. 220

C. 230

D. 240

Answer
Verified

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

__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 \[\dfrac{n(n+1)}{2}\].

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{align}

& \Rightarrow \dfrac{n(n+1)}{2} \\

& \Rightarrow \dfrac{20(20+1)}{2} \\

& \Rightarrow 10(21) \\

& \Rightarrow 210 \\

\end{align}\]

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. $S_n = \dfrac{n}{2} [2a+(n-1)d]$ where first term (a) = 1, common difference (d) =1 and n =20.

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 \[\dfrac{n(n+1)}{2}\].

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{align}

& \Rightarrow \dfrac{n(n+1)}{2} \\

& \Rightarrow \dfrac{20(20+1)}{2} \\

& \Rightarrow 10(21) \\

& \Rightarrow 210 \\

\end{align}\]

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. $S_n = \dfrac{n}{2} [2a+(n-1)d]$ where first term (a) = 1, common difference (d) =1 and n =20.

×

Sorry!, This page is not available for now to bookmark.