Question

find three consecutive even integers such that two times the second equals the sum of the first and third

Answer 1

We are asked to determine three consecutive even integers. Let those integers be:

`n_1,n_2,n_3`

Since the integers are consecutive we have the following relationships:

`\begin{gathered} n_2=n_1+2 \\ n_3=n_1+4 \end{gathered}`

We are also given that two times the second equals the sum of the first and third. This can be expressed mathematically as:

`2n_2=n_1+n_3`

Now we can substitute the value of n3 from the previous relationship:

`2n_2=n_1+n_1+4`

Adding like terms:

`2n_2=2n_1+4`

We can also substitute the value of n3:

`2(n_1+2)=2n_1+4`

We get:

`2n_1+4=2n_1+4`

This is valid for any "n". Therefore any three consecutive integers are a solution.