Five consecutive odd numbers have a total sum of 175. Identify the second-largest number, square the smallest number, and report the sum of these two results.

Introduction / Context:This question combines sequences with arithmetic operations. Consecutive odd numbers centered on a middle term add up conveniently, enabling fast recovery of the five terms. Then we perform the requested operations to obtain the final sum.

Given Data / Assumptions:

• Five consecutive odd integers sum to 175.
• We need: (second-largest) + (smallest)^2.
• Consecutive odd numbers are equally spaced with common difference 2.

Concept / Approach:For five consecutive odds written as n−4, n−2, n, n+2, n+4, the sum is 5n. This determines the middle term immediately. Then list the set, pick out the smallest and second-largest, compute the square and the addition.

Step-by-Step Solution:Let the five numbers be n−4, n−2, n, n+2, n+4.Sum = 5n = 175 → n = 35.Thus the numbers are 31, 33, 35, 37, 39.Smallest = 31; second-largest = 37.Compute 31^2 = 961; add 37 to get 961 + 37 = 998.

Verification / Alternative check:Recheck the list and positions: second-largest is indeed 37 (only 39 is larger). The arithmetic 961 + 37 gives 998 consistently.

Why Other Options Are Wrong:989, 997, and 979 are close distractors but do not match the exact computation. Since 998 is not listed among the main options, “none of the above” is correct.

Common Pitfalls:Picking the largest instead of second-largest; squaring the wrong term; using even numbers or mis-centering the five odds.

Final Answer:none of the above