Question

The sum of the first 10 natural number is,
A. 100
B. 55
C. 50
D. 90

Answer 1

First, start by identifying and writing the first 10 natural numbers and look for the sequence formed I.e. Arithmetic progression and distinguish the first term, common difference, and the total number of terms, apply the general formula for the sum of first n terms of an A.P. and simplify for the final answer.

Complete step-by-step solution:
In order to find the sum of the first 10 natural numbers first of all we have to find the first 10 natural numbers.
And we know the first 10 natural numbers are 1, 2, 3, ……. 9, 10.
So now clearly if you see they are in AP (arithmetic progression)
Whose first term is $a = 1$ and the common difference is $d = 1$.
Let ${S_n}$ denote the sum of first n natural numbers. The formula is,
${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$
Where $a$ is the first term and $n$ is the number of terms and $d$ is the common difference.
Substituting all the values of $a,d,n$, we get
$\Rightarrow {S_{10}} = \dfrac{{10}}{2}\left[ {2 \times 1 + \left( {10 - 1} \right) \times 1} \right]$
Simplify the terms,
$\Rightarrow {S_{10}} = 5 \times \left( {2 + 9} \right)$
Add the terms in the bracket,
$\Rightarrow {S_{10}} = 5 \times 11$
Multiply the term,
$\therefore {S_{10}} = 55$
Thus, the sum of the first 10 natural numbers is 55.
Hence, option (B) is correct.

Note: Whenever we face such types of problems, we use some important points. We can see the formula of the sum of first n natural numbers mentioned in the question is the same as the formula of the sum of first n terms of A.P. So, put the value of sum in the formula and then after doing some calculation we can get the required answer.