Consecutive Odd Integers — Sum Given The sum of three consecutive odd integers is 57. Identify the middle (second) integer among them.

Introduction / Context:
Consecutive odd integers are evenly spaced by 2. When three such numbers are added, the middle one equals their average, which dramatically simplifies the calculation. This question examines your ability to translate a verbal description into a compact algebraic form and compute accurately.

Given Data / Assumptions:

• There are three consecutive odd integers.
• Their sum is 57.
• We need the middle integer.

Concept / Approach:
Let the middle odd integer be n. Then the three consecutive odds are n − 2, n, and n + 2. Their sum becomes (n − 2) + n + (n + 2) = 3n. Setting 3n = 57 yields n directly. This approach avoids listing numbers and reduces the task to a single division.

Step-by-Step Solution:
Let the three numbers be n − 2, n, n + 2.Sum = 3n = 57.Solve for n: n = 57 / 3 = 19.Therefore, the middle integer is 19.

Verification / Alternative check:
List them explicitly: 17, 19, 21. Sum = 17 + 19 + 21 = 57. The middle is indeed 19.

Why Other Options Are Wrong:
21 and 23 are neighboring odd numbers but would yield sums 63 and 67 respectively; 17 is the smallest, not the middle; 15 lies outside the valid triple for sum 57.

Common Pitfalls:
Using step 1 instead of step 2 (confusing consecutive integers with consecutive odd integers); adding wrong or mixing positions (smallest vs middle).

Final Answer:
19