Question

Find the sum of the first $100$ natural numbers.

Answer 1

Find the sum of the first 100 natural numbers.

The formula to calculate the sum of $n$ natural numbers.

$S_n=\frac{n}{2}(a+a_n)$

$S_n$ is the sum of the arithmetic sequence,

$a$ is the first term,

$d$ the common difference between the terms,

$n$ is the total number of terms in the sequence and

$a_n$ is the last term of the sequence.

Here $a=1$

$a_n=100,n=100$

$$\begin{gathered} \Rightarrow S_n=\frac{100}{2}(1+100) \\ \Rightarrow S_n=\frac{100}{2}\times \left(101\right) \\ \Rightarrow S_n=50\times 101 \\ \Rightarrow S_n=5050. \end{gathered}$$

Hence, the sum of first $100$natural numbers is $5050$.