The sum of four consecutive even integers is 284. What is the smallest of these even integers?

Introduction / Context:Consecutive even integers form an arithmetic sequence with common difference 2. Summation and simple algebra quickly identify the first term when the total is known.

Given Data / Assumptions:

• Let the four numbers be x, x + 2, x + 4, x + 6.
• Their sum equals 284.
• All are even integers by construction.

Concept / Approach:Use linear equations for arithmetic sequences. The sum is 4x + 12; isolate x to get the smallest integer directly.

Step-by-Step Solution:

Verification / Alternative check:Average method: the average of four equally spaced numbers is the mean of the first and last: (68 + 74) / 2 = 71. Multiply by count: 71 * 4 = 284; matches.

Why Other Options Are Wrong:66, 70, 72, or 74 would yield sums different from 284 when building the required four-term set.

Common Pitfalls:Using difference 1 instead of 2 (confusing even with consecutive integers in general).

Final Answer:68