The average of 5 consecutive odd positive integers is 9. What is the least of these integers?

Introduction / Context:For any odd-count set of consecutive odd integers, the average equals the middle term. From that center, list the two preceding and two following odds to identify the least value.

Given Data / Assumptions:

• Five consecutive odd positive integers.
• Average = 9 ⇒ middle term = 9.

Concept / Approach:Consecutive odd integers differ by 2. With middle 9, the sequence is 9 − 4, 9 − 2, 9, 9 + 2, 9 + 4. The least is the smallest of that set.

Step-by-Step Solution:

Verification / Alternative check:Average of 5 and 13 is (5 + 13) / 2 = 9, matching the given mean; the set is symmetric around 9.

Why Other Options Are Wrong:3 and 1 are too small; 7 is not the least in the sequence; “None of these” is unnecessary since 5 is correct.

Common Pitfalls:Using even spacing of 1 (integers) rather than spacing of 2 (odd integers), which would misplace endpoints.

Final Answer:5