Question

The sum of first $$45$$ natural numbers is:
A). $$1035$$
B). $$1075$$
C). $$2045$$
D). $$2076$$

Answer 1

Hint: In the given question, we have been given to find the sum of the first given number of natural numbers. We do not have to do that by adding each number. There is a formula for doing the same operation. We just need to remember the formula, plug in the given number of first some natural numbers, solve the calculation and we get the answer.

Formula used:
We are going to use the following formula:
The sum of first $$n$$ natural numbers is,
$$S_n={\displaystyle \frac{n\left(n+1\right)}{2}}$$

Complete step by step solution:
We have to find the sum of first $$45$$ natural numbers.
We are going to use the following formula for the sum of first $$n$$ natural numbers which is,
$$S_n={\displaystyle \frac{n\left(n+1\right)}{2}}$$
Putting in $$n=45$$, we have,
$$S_{45}={\displaystyle \frac{45\left(45+1\right)}{2}}={\displaystyle \frac{45\times 46}{2}}=45\times 23=1035$$
Hence, the correct option is (A).

Additional Information:
Here we had to find the sum of first $$n$$ natural numbers. If we had to find the sum of square of first $$n$$ natural numbers or the sum of cube of first $$n$$ natural numbers, then we would have used the following formulae respectively:
$$S_{n^2}={\displaystyle \frac{n\left(n+1\right)\left(2n+1\right)}{6}}$$ and $$S_{n^3}={\left({\displaystyle \frac{n\left(n+1\right)}{2}}\right)}^2$$

Note: In the given question, we had to find the sum of first some given natural numbers. We did that by using the formula designed to do the same. We just need to remember the formula, put in the given number, solve the operation, and get our answer. If we do not remember the formula, then it would be a problem as adding each number is very lengthy and tiring.