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

Introduction / Context:
Consecutive even integers increase by 2 each time. Summation of such a group forms a quick linear equation. This tests modeling skills and careful arithmetic.

Given Data / Assumptions:

• The four even numbers are consecutive: a, a + 2, a + 4, a + 6.
• Their total sum is 284.
• We must find the smallest, a.

Concept / Approach:
Write the sum in terms of a and equate to 284. Because the common difference is 2, the sum is 4a + 12. Solve the resulting linear equation for a.

Step-by-Step Solution:
Sum: a + (a + 2) + (a + 4) + (a + 6) = 284.Combine like terms: 4a + 12 = 284.Subtract 12: 4a = 272.Divide by 4: a = 68.

Verification / Alternative check:
Numbers are 68, 70, 72, 74. Sum = 68 + 70 + 72 + 74 = (68 + 74) + (70 + 72) = 142 + 142 = 284. Checks out.

Why Other Options Are Wrong:
66 and 70 are near misses that give totals not equal to 284; 72 and 74 are not the smallest in the valid set.

Common Pitfalls:
Using odd increments of 1 instead of 2; arithmetic slips when subtracting 12; misidentifying the smallest number after solving.

Final Answer:
68