Let the three consecutive integers be represented as:

• $n-1$ (the integer before $n$),
• $n$ (the middle integer),
• $n+1$ (the integer after $n$).

The sum of these three integers is:

$(n-1) + n + (n+1)$

Simplifying this expression:

$(n-1) + n + (n+1) = n-1 + n + n+1 = 3n$

Thus, the expression for the sum of the three consecutive integers is $3n$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the sum of three consecutive integers when the middle number is 5?
2. How would you find the middle number if the sum of the three consecutive integers is 27?
3. What happens if you add four consecutive integers instead of three?
4. Can the sum of three consecutive integers ever be an odd number?
5. How can you represent the product of three consecutive integers using $n$?

Tip: When dealing with consecutive numbers, their sum or differences often simplify due to the symmetry in their values.