Let “n” be the middle number for three consecutive even integer. Write an expression for the sum of these integers 

Let's break this down.

Let the three consecutive even integers be represented by:

- The middle integer is \( n \).
- The even integer before \( n \) would be \( n - 2 \) (since the integers are even and consecutive).
- The even integer after \( n \) would be \( n + 2 \).

Now, the sum of these three integers would be:

\[
(n - 2) + n + (n + 2)
\]

Simplifying this expression:

\[
(n - 2) + n + (n + 2) = n - 2 + n + n + 2 = 3n
\]

So, the expression for the sum of three consecutive even integers where \( n \) is the middle number is:

\[
\boxed{3n}
\]

If you have any questions or need further clarification, feel free to ask!

Here are some follow-up questions for further exploration:
1. What would be the sum if \( n = 4 \)?
2. How would the expression change if we were dealing with consecutive odd integers?
3. Can you find a general formula for four consecutive even integers?
4. What happens to the sum if the integers were consecutive multiples of 3?
5. How can this expression be used in a real-world scenario?

**Tip:** Always ensure that you check if you’re dealing with consecutive even or odd integers, as this changes the approach slightly.

Explore how to calculate the sum of three consecutive even integers using a step-by-step approach. Learn the formula and method for finding the sum of these integers, suitable for middle school students (Grades 6-8).

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