Question

Calculate the sum of natural numbers between 1 and 42.
A) 460
B) 900
C) 903
D) 920

Answer 1

We are given the two limits as 1 and 42. But here we are not going to literally add the numbers rather we will use the formula for finding the sum of n natural numbers.
$sum = \dfrac{{n\left( {n + 1} \right)}}{2}$ where n is the numbers to be added. Let’s solve it!

Complete step by step solution:
Given that there are 42 numbers in 1 and 42. So n=42.
Now using the formula mentioned above
$sum = \dfrac{{n\left( {n + 1} \right)}}{2}$
$\Rightarrow \dfrac{{42\left( {42 + 1} \right)}}{2}$
Divide 42 by 2 and add the numbers in bracket
$\Rightarrow 21 \times 43$
On multiplying we get
$\Rightarrow 903$
Hence 903 is the sum of natural numbers between 1 and 42.
**
So the correct option is C.**

Note:
Alternate method:
Given numbers are in an arithmetic series like a sequence we can say. Where first term a=1 and common difference d=1. Isn’t it??
So e can use the formula of sum of terms of an arithmetic series as
${S_n} = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$
Here a=1, d=1. So, it becomes
${S_n} = \dfrac{n}{2}\left( {2 + \left( {n - 1} \right)} \right)$
$\Rightarrow {S_n} = \dfrac{n}{2}\left( {n + 1} \right)$
And this is the same formula we used above.
$\Rightarrow {S_n} = \dfrac{{42}}{2}\left( {42 + 1} \right) = 21 \times 43 = 903$