The sum of three consecutive even integers is 102. What is the largest integer? - AIKO, infinite ways to autonomy.
The Sum of Three Consecutive Even Integers Is 102. What Is the Largest Integer?
The Sum of Three Consecutive Even Integers Is 102. What Is the Largest Integer?
Finding the largest of three consecutive even integers that add up to 102 can be a fun and rewarding math puzzle—whether you're a student learning algebra, a teacher illustrating number patterns, or someone who simply enjoys practicing logic. In this article, we’ll walk through the steps to solve this problem clearly and confidently.
Understanding Consecutive Even Integers
Understanding the Context
Consecutive even integers are numbers that follow one after the other in the sequence of even numbers, increasing by 2. For example, if one integer is n, then the next two consecutive even integers are n + 2 and n + 4.
We are told the sum of three such consecutive even integers equals 102:
n + (n + 2) + (n + 4) = 102
Step-by-Step Equation Solution
- Combine like terms:
Add the expressions:
n + (n + 2) + (n + 4) = 3n + 6
Image Gallery
Key Insights
So, the equation becomes:
3n + 6 = 102
- Solve for n:
Subtract 6 from both sides:
3n = 96
Divide both sides by 3:
n = 32
- Find the three integers:
The middle number is 32. Therefore:
- First even integer: 32
- Second even integer: 32 + 2 = 34
- Third (largest) even integer: 32 + 4 = 36
Verify the Sum
🔗 Related Articles You Might Like:
📰 This Simple Act Transforms Your World—Do You Have What It Takes? 📰 When Your Pedestal Cracks—Everything Fails, and Here’s the Shocking Fix 📰 Peoplesearchnow Exposes Secrets You Didn’t Know You Needed to See 📰 Kick Movie Kick 7800725 📰 Open Banking Seo Goldmine Exposed Our Unbelievable Open Bank Reviews 9399781 📰 You Wont Believe What Happened When Gokuto Went Viral Shocking Secrets Inside 6838333 📰 I Ate The Soft Serve And Now Im Never Eating Regular Ice Cream Again 9202737 📰 Jobeth Williams 9520103 📰 Versalink B405 Driver 9786131 📰 The Echoes Of The Forbidden Cavern Alarms You Never Should Have Heard 4887543 📰 Dont Blinkprmovies Are Here To Steal Your Night 5485198 📰 Crossy Roads 8927301 📰 From Whisper To Shockwaveyou Wont Believe How This Voice Changer Girl Changed The Game 5711456 📰 Why Top Companies Choose Azure Logos Shocking Symbols You Need To Know 6115571 📰 You Wont Believe How Old Flavor Flav Really Ishistory Of The Iconic Mask Unveiled 6364820 📰 Where To Watch New Orleans Saints Vs Chicago Bears 410010 📰 Lottery Winnter 6703758 📰 How A Small Irs Move By Judge Kollar Kotelly Unleashes A Legal Cosmic Failure 5062139Final Thoughts
Let’s check:
32 + 34 + 36 = 102 ✅
That confirms our solution is correct.
Final Answer
The largest of the three consecutive even integers is 36.
This simple yet powerful problem reinforces basic algebraic thinking, helps identify patterns in number sequences, and demonstrates how to translate words into equations. Next time you encounter three consecutive even integers summing to a known value, you’ll know exactly how to find the largest with ease!
