# The sum S of first n natural numbers is given by S = n(n + 1) / 2. If S = 231, find n.

Natural Numbers can be considered the backbone of mathematics. Almost all the numbers which we deal with in real life are natural numbers. The natural numbers start from one and can go up to infinite values. We can also find the sum of consecutive natural numbers directly by using a formula. Let's find out how.

## Answer: The value of n when the sum of natural numbers S = 231 is n = 21.

Let's see how we found the solution.

**Explanation:**

It is given that the sum of n consecutive natural numbers is given to be S = n(n + 1)/2.

If S = 231, then we have to solve the equation n(n + 1)/2 = 231 to get the value of n.

Hence, rearranging the equation, we get n^{2} + n - 462 = 0.

Now, we have to solve the quadratic equation.

After solving the equation we get, n = 21, -22.

Since -22 is negative, and n can only be positive as it is the number of terms, it is rejected. We consider only n = 21.