# Math Help - Variation problem

1. ## Variation problem

The sum of the first $n$ natural numbers is equal to the sum of two quantities, the first of which is proportional to $n$ and the second to $n^2$. Work out the sums of the first three and four natural numbers and hence find the formula for the sum of the first $n$ natural numbers.

How do I do this?

2. Originally Posted by jgv115
The sum of the first $n$ natural numbers is equal to the sum of two quantities, the first of which is proportional to $n$ and the second to $n^2$. Work out the sums of the first three and four natural numbers and hence find the formula for the sum of the first $n$ natural numbers.