The sum of three consecutive even integers is 102. What is the largest integer? - inBeat
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:
📰 nfl who's playing tonight 📰 grey griffin 📰 scooby doo show 📰 Alineaciones De Manchester City Contra Newcastle 7529000 📰 Gummy Bears By The Brand Which One Is The Most Irresistibly Delicious 7945306 📰 Garbage Bags 44744 📰 Vivian Jenna Wilson Siblings 4602882 📰 360 Schedule 6735010 📰 Mac Download 595255 📰 Surface Laptop Studio 2 The Ultimate Studio Perfect Laptop Thats Taking Over Workspaces 5026345 📰 God Bless The Usa Song 2913927 📰 Package B Total 48000 15 Of 48000 48000 7200 55200 3721740 📰 You Wont Believe What Happens When You Go Through The Transverse Plane The Ultimate Body Transformation 4497374 📰 Best Non Alcoholic Wine 9286009 📰 What Is Fate 600544 📰 Calculator For Car Loans 8616160 📰 Mortgage Calculator Montana 6033203 📰 Master Cache Pronunciation In Seconds No More Confusion Ever 5209900Final 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!
