Five consecutive odd numbers: If the numbers are a, a+2, a+4, a+6, and a+8, what is their average in terms of a?

Introduction / Context:For equally spaced numbers (an arithmetic progression), the average equals the middle term. Five consecutive odd numbers centered around the third term follow this rule directly.

Given Data / Assumptions:

• Numbers: a, a+2, a+4, a+6, a+8
• Common difference = 2

Concept / Approach:The average of an arithmetic progression equals (first + last) / 2. With an odd count, it also equals the middle element.

Step-by-Step Solution:

Verification / Alternative check:Pick a = 1. The set is 1, 3, 5, 7, 9. Average = 25 / 5 = 5. Middle term = 5 = 1 + 4.

Why Other Options Are Wrong:

• (a + 8) / 2: ignores symmetry and double counts incorrectly.
• (a + (a+8)) / 2 is algebraically equal to a + 4, but many candidates misuse parentheses; we use the simpler a + 4 as the canonical form.
• (a + 2 + a + 4 + a + 6) / 5 omits two terms and is incomplete.
• a + 5 is off by one from the correct midpoint.

Common Pitfalls:Forgetting to average first and last or not recognizing the middle term identity for an odd count.

Final Answer:a + 4