Question

The sum of two consecutive natural numbers is 525.
Find the numbers.

Answer 1

262 and 263 are consecutive natural numbers whose sum is 525.

Explanation:

Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (
`|x-y| = 1`,
`\forall\,x,y \in \mathbb{N}`) We can interpret the statement mathematically by means of the following expression:

`x + y = 525`

`x = n`

`y = n+1`

Where
`x`,
`y`,
`n`
`\in \mathbb{N}`.

This system is reduced to a single equation and solved afterwards:

`n +(n+1) = 525`

`2\cdot n + 1 = 525`

`2\cdot n = 524`

`n = 262`

Now we evaluate
`x` and
`y` to obtain the natural numbers:

`x = 262`

`y = 263`

262 and 263 are consecutive natural numbers whose sum is 525.