The sum of three consecutive even integers is 90. What is the largest of these integers? - Treasure Valley Movers

Understanding the Sum of Three Consecutive Even Integers: What Is the Largest?

When you encounter a problem like “The sum of three consecutive even integers is 90,” it’s more than just a math puzzle—it’s a gateway to understanding sequences, algebra, and logical reasoning. In this article, we’ll solve the equation step-by-step and reveal how to find the largest of these integers. Whether you're a student, a teacher, or someone curious about number patterns, this is a clear and practical guide.

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What Are Consecutive Even Integers?

Consecutive even integers are numbers like 2, 4, 6 or 14, 16, 18 — each differing by exactly two. Because even numbers are always two units apart, finding three in sequence is straightforward: if the first is n, the next two are n+2 and n+4.

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Setting Up the Equation

Let the first even integer be:
n

Then the next two consecutive even integers are:
n + 2 and n + 4

The sum of these three integers is given as 90:
n + (n + 2) + (n + 4) = 90

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Solving the Equation Step-by-Step

1. Combine like terms:
   3n + 6 = 90

2. Subtract 6 from both sides:
   3n = 84

3. Divide both sides by 3:
   n = 28

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Identifying All Three Integers

Now that we know n = 28, the three consecutive even integers are:

• First: 28
  
• Second: 30
  
• Third (largest): 32

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Verifying the Solution

Let’s check:
28 + 30 + 32 = 90 ✅
All numbers are even and consecutive in sequence ✅
The largest is indeed 32 ✔️

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