The sum of three consecutive even integers is 102. What is the largest integer? - Tacotoon
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:
📰 Maxi Cosi Car Seat Exposed—No Hidden Flaws, Only Practical Brilliance 📰 This Maxi Cosi Car Seat Is a Must-Have For Every Parent’s Top Pick 📰 The Secret Maximal Restaurant That Outshines Every Dining Spot Ever 📰 You Wont Believe How Common This Broken Screen Wallpaper Chaos Actually Is 📰 You Wont Believe How Cool The Caesar Cut Haircut Looks On Men Try It Now 📰 You Wont Believe How Cool These Bow Jeans Look On Any Lookshop Now 📰 You Wont Believe How Cool This Boys Suit Looksboys Are Turning Heads 📰 You Wont Believe How Cool This Bubble Letter D Looks Go Viral With It 📰 You Wont Believe How Cool This Bubble Letter S Is Try It Today 📰 You Wont Believe How Costume Pants For Men Blend Perfectly Into Every Scene 📰 You Wont Believe How Cozy These Melville Sweatpants Feelbrandy Melville Sweatpants That Slay Every Look 📰 You Wont Believe How Cozy This Brown Essentials Hoodie Feelsstyle Meets Comfort 📰 You Wont Believe How Crave Worthy Cajun Fries Dominate The Culinary Scene 📰 You Wont Believe How Creative C In Cursive Looks When Styled Perfectly 📰 You Wont Believe How Crispy Brats Get In This Air Fryer Hacks 📰 You Wont Believe How Crispy Breaded Pork Chops Cook In The Ovenwatch This 📰 You Wont Believe How Crispy These Brats Get In The Air Fryer Top Secret Recipe Revealed 📰 You Wont Believe How Crispy This Breaded Chicken Melting Melt Will Transform Your DinnerFinal 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!
