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:

📰 Discover Olivia Munn’s Hidden Gems: The Astonishing Movies and TV Shows You’ve Missed! 📰 Olivia Munn’s Most Shockingly Talented Film & TV Roles You Need to Watch Now! 📰 Breaking: Olivia Munn’s Surprisingly Iconic Movies & TV Appearances That Defied Expectations 📰 The Barber Pole Million Dollar Secret Ringing Through Every Trim 📰 The Barber Pole That Whispers Truths You Never Wanted To Hear 📰 The Barbie Cake Thats Sparkling Sweet And Perfectly Themed To Stun 📰 The Bare Truth Inside Beyoncs Most Shocking Exposed Unfiltered Scene 📰 The Bare Version Real Feelings In Baile Inolvidables English Lyrics Nothing Hidden 📰 The Baritone Saxophone That Will Make You Scream When You Play It 📰 The Barn Jacket That Makes Every Outing Feel Like Rural Coolstep Into The Hype 📰 The Barn Jacket That Turned Heads At The Farmers Marketyoull Need It Before Fall 📰 The Barndominium Youve Always Dreamed Of But Never Imagined Selling 📰 The Barongs Whisper Protects Secrets She Keeps Forever 📰 The Barrel Chair No One Talks Aboutbut Everyone Needs Now 📰 The Basketbros Betrayal That Shook The Entire Basketball Community 📰 The Bass Amp That Made Pro Players Cry Againno One Sees It Coming 📰 The Bass Amp That Transformed Your Gear Into Pure Firepower 📰 The Bass Tuner Thats Upending Musicbecause Your Tone Deserves Faithfulness

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 ✔️