The sum of three consecutive even integers is 90. What is the largest of these integers? - GetMeFoodie
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
Image Gallery
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:
📰 This Pocket of Happiness Is Macadoodles—Stop Treating Yourself Like Normal Food 📰 Are Macaroons Outlisting Macarons in the Sweet Caramel Showdown? 📰 Macarons or Macaroons? The Ultimate Debate Overworld’s Favorite Treat 📰 Asian Onlyfans 8571877 📰 Amazon Shoe Storage 8079106 📰 A Reforestation Project Plants 3000 Trees In The First Year Each Year The Number Planted Increases By 20 How Many Trees Are Planted In The Third Year 6018128 📰 Amber Smith 8510 📰 Frances Best Wine Secrets Revealedwhat Makes These Regions Unforgettable 7384723 📰 Singing Machine Karaoke 📰 Celebrity Ai Voice Generator 6715289 📰 Major Breakthrough Sp500 Stock Price And It Alarms Experts 📰 A Renewable Energy Analyst Estimates That A New Solar Farm Will Generate 48 Gigawatt Hours Gwh Annually If Each Household Uses 8000 Kwh Per Year How Many Households Can The Solar Farm Power Each Year 8939948 📰 They Stumbled Upon Texasmaniaand Everything Changed Forever 2117049 📰 Boa Relationship Manager 📰 Finally Logged Inyour Cricket Rewards Await Everyone 7717701 📰 Sudden Change Lyrics Of Demons Song And Experts Investigate 📰 Lbc Tracking What Everyones Missing That Will Change Your Shipping Game 1170183 📰 Oracle Data SecurityFinal 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 ✔️
