Question

The sum of first $20$ natural numbers is
A) 55
B) 210
C) 110
D) 215

Answer 1

Here we will use the sum of the $n$ natural numbers formula we will get the answer for the given question. In question give the value for $n$ . We will substitute value for $n$ in the given formula we will get the answer for this question.

Formula used: ${S_n} = \dfrac{{n(n + 1)}}{2}$

Complete step by step solution:
We have to find the sum $n$ terms of the AP(Arithmetic Progression) $= 1,2,3,.....$
Here
$a = 1,d = 1$
Here $a$ is the first term.
and $d$ is a common difference.
$n$ is the total number of terms.
Therefore, required sum
${S_n} = \dfrac{n}{2}[2a + (n - 1)d] = \dfrac{n}{2}[2 \times 1 + (n - 1) \times 1] \\\ \Rightarrow {S_n} = \dfrac{n}{2}[2 + n - 1] \\\$
Above terms are simplify finally we got the formula
Therefore, the formula is ${S_n} = \dfrac{{n(n + 1)}}{2}$
Apply the parameter values in the formula.
We will put them $n = 20$ in given formula
${S_{20}} = \dfrac{{20\left( {20 + 1} \right)}}{2} \\\ {S_{20}} = \dfrac{{20 \times 21}}{2} \\\$
Simplify the above equation and we will get the answer.
${S_{20}} = \dfrac{{420}}{2} = 210$

Here the answer is Option (B).

Note: There is no largest natural number. The next natural number can be found by adding one to the current natural number, producing numbers that go on "forever". There is no natural number that is infinite in size. Any natural number can be reached by adding one enough time to the smallest natural number. The natural numbers are used to counting and the ordering purpose. The sum or product of natural numbers are also natural numbers.
They are the numbers you usually count and they will continue on into infinity. Whole numbers are all-natural numbers including $0$.The set of natural numbers that includes zero is known as the whole numbers. A set of whole numbers are typically denoted by $W$. Natural numbers must be whole and positive. This makes sense for a number of reasons, including the fact that they are counting numbers.