Answered

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

Sagot :

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

[tex]n_1,n_2,n_3[/tex]

Since the integers are consecutive we have the following relationships:

[tex]\begin{gathered} n_2=n_1+2 \\ n_3=n_1+4 \end{gathered}[/tex]

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

[tex]2n_2=n_1+n_3[/tex]

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

[tex]2n_2=n_1+n_1+4[/tex]

Adding like terms:

[tex]2n_2=2n_1+4[/tex]

We can also substitute the value of n3:

[tex]2(n_1+2)=2n_1+4[/tex]

We get:

[tex]2n_1+4=2n_1+4[/tex]

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

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