If \( n \) represents a positive integer, then the expression for three consecutive integers can be written as:
- The first integer: \( n \)
- The second integer: \( n + 1 \)
- The third integer: \( n + 2 \)
Therefore, the algebraic expressions for three consecutive integers are \( n \), \( n + 1 \), and \( n + 2 \).