Express the given quantity in terms of the indicated variable.
The sum of four consecutive even integers;  n = first integer of the four

The problem asks us to express the sum of four consecutive even integers in terms of \( n \), where \( n \) is the first integer.

Consecutive even integers differ by 2. So, if \( n \) is the first even integer, the next three even integers would be:

- First integer: \( n \)
- Second integer: \( n + 2 \)
- Third integer: \( n + 4 \)
- Fourth integer: \( n + 6 \)

Now, to find the sum of these four integers, we simply add them together:

\[
n + (n + 2) + (n + 4) + (n + 6)
\]

Simplify the expression:

\[
n + n + 2 + n + 4 + n + 6 = 4n + 12
\]

So, the sum of the four consecutive even integers is \( 4n + 12 \).

### Final Answer:
The sum of four consecutive even integers in terms of \( n \) is \( 4n + 12 \).

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Would you like more details on any part of the explanation?

Here are 5 related questions to explore further:

1. What is the sum of four consecutive odd integers, starting with \( n \)?
2. How can you find the product of four consecutive even integers starting with \( n \)?
3. If the sum of four consecutive even integers is 100, what is the value of \( n \)?
4. How would the sum change if the integers were consecutive odd integers instead of even?
5. How can you generalize this approach for any number of consecutive even integers?

**Tip**: When dealing with sequences, it's helpful to define variables clearly and recognize consistent patterns in how they progress!

The sum of four consecutive even integers; n = first integer of the four

Understand how to express the sum of four consecutive even integers, starting with n, in terms of n. This solution covers key algebraic concepts and the arithmetic sequence sum formula, making it ideal for students in Grades 6-8.

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