The sum of three consecutive even integers is 90. What is the largest of these integers?

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

The sum of three consecutive even integers is 90. What is the largest of these integers?

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:

📰 south paul the movie 📰 south pole jeans 📰 southern comfort eggnog 📰 This Momo Clip Left Me Tremblingis This Real Or Just A Nightmare 📰 This Money Obscures Doomevery Secret Fire Betrays The Vc Plot 📰 This Monopoly Go Hack Will Ruin Any Beginners Game Forever 📰 This Monster House Cast Changed Everythingdont Miss The Unthinkable Truth 📰 This Monster Squad Invades Your Nighthome Invasion Like Youve Never Seen Before 📰 This Monte Carlo Film Will Rewrite Your Understanding Of Fate And Chance 📰 This Montefiore Chart Will Change How You See Your Medical History Forever 📰 This Moon Sign Mastery Will Change How You Love Forever 📰 This Morning Feast From Hardees Has Everyone Snapping Unbelievable Flavor 📰 This Morse Translator Was Designed For Surprisescan You Handle The Revelations 📰 This Mortal Kombat Quest Has Crushed Legacy Fighters In An Unstoppable Warlord Onslaught 📰 This Mot Checker Finds Out What Your Words Always Hide 📰 This Mothers Unfiltered Journey Exposes The Messy Real Truth No One Explains 📰 This Mountain Project Could Unlock Secrets That Were Suppressed For Decades 📰 This Movie Ate Your Heartdo You Really Want To Watch

Final 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 ✔️