The sum of three consecutive even integers is 90. What is the largest of these integers? - Decision Point
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:
📰 How to Turn Roaming Off on an Iphone 📰 Cast of the Presidio 📰 Tv Shows with Chanel West Coast 📰 What Animal Seriously Impersonates Arthur You Wont Believe The Answer 2824039 📰 Cbp One Asylum Appointments Cancelled 9416090 📰 Digitalis Digitalis Alone Poisoned Your Health You Wont Believe The Shocking Truth 9036638 📰 Perhaps The Question Has A Typo And The Desired Average Is 14 Not 45 But We Must Answer 5426736 📰 Suicid Squad 2 7330075 📰 Kim On Kanye 8834440 📰 Life The Game Discover The Hidden Rules That Will Change How You Live Forever 2081763 📰 The Man The Numbers The Momentlebrons 20 Stuns The World 5410271 📰 Mexico Vs Argentina 2025 3547847 📰 V Mathematics 4694369 📰 David Caprio 4802966 📰 Hyatt Uptown 6409899 📰 Tiger Tiger Games The Secret Game Everyones Been Whispering About Act Now 5430856 📰 Heb Eggs 2468707 📰 Heating Up The Court How Warriors And Heat Players Blaze Stats In Sample Clash 2933702Final 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 ✔️
