write expressins representing three consecutive even integers  

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to write a reccurence relation that allows you to evaluate any three consecutive even integers, such that:

`n - 2, n, n + 2`

You should notice that a sequence of three consecutive numbers means a combination of two even numbers and one odd or two odds and one even. You need to get a sequence of three even integers, hence, you need to use the definition of an arithmetical progression whose common difference is `d = 2` , such that:

`n = (n - 2 + n + 2)/2 => n = (2n)/2 => n = n`

Hence, you may use the following reccurence relation to describe a sequence of three consecutive even terms, such that `a_n = a_(n - 2) + 2.`

revolution | Student

For example, let say 2 is the first number

If you need a even number to be your second number, then you have to add 2 to the number which means 2+2=4. For the third number, you have to do the same thing (4+2=6).

Which means, in algebraic expressions:

 The first number would be represented as X

 The second number would be represented as X+2

The third number would be represented as X+2+2= x+4

cmarshall1974 | Student

For any given even value of "x" you can find its consecutive even integers by substituting the value of x in and simplyfing into the following expressions