The sum of three consecutive even integers is 90. What is the largest of these integers? - Leaselab
Understanding the Sum of Three Consecutive Even Integers: What Is the Largest?
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.
Understanding the Context
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.
Setting Up the Equation
Key Insights
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
Solving the Equation Step-by-Step
🔗 Related Articles You Might Like:
Sahaviriya Steel Industries Revealed: The Brazen Betrayal That Producer’s Refused to Ignore Silent Takeover or Steel Complex’s Final Threat? Sahaviriya Steel Speaks Out Today How Sahaviriya Steel Industries Is Ruining Competitors from Inside—The Untold Story ExposedFinal Thoughts
-
Combine like terms:
3n + 6 = 90 -
Subtract 6 from both sides:
3n = 84 -
Divide both sides by 3:
n = 28
Identifying All Three Integers
Now that we know n = 28, the three consecutive even integers are:
- First: 28
- Second: 30
- Third (largest): 32
Verifying the Solution
Let’s check:
28 + 30 + 32 = 90 ✅
All numbers are even and consecutive in sequence ✅
The largest is indeed 32 ✔️
