The Pattern of Adding Consecutive Even Numbers from 2 to 100
Have you ever wondered what would happen if you started adding consecutive even numbers starting from 2 and continued all the way up to 100? Let's dive into this interesting mathematical exploration and see what pattern emerges.
The Sequence
The sequence of adding consecutive even numbers from 2 to 100 would look like this:
2 + 4 + 6 + 8 + 10 + ... + 100
Let's calculate the sum of the first few terms to see if we can identify a pattern:
- 2 + 4 = 6
- 2 + 4 + 6 = 12
- 2 + 4 + 6 + 8 = 20
- 2 + 4 + 6 + 8 + 10 = 30
The Pattern Emerges
As we continue adding more terms, we start to notice a striking pattern. The sum of the consecutive even numbers is increasing by 10 each time!
- 2 + 4 + 6 + 8 + 10 + 12 = 40
- 2 + 4 + 6 + 8 + 10 + 12 + 14 = 50
- 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 = 60
- ...
This pattern continues all the way up to 100. Let's calculate the final sum:
2 + 4 + 6 + 8 + 10 + ... + 100 = 550
The Formula
By examining the pattern, we can derive a formula to calculate the sum of consecutive even numbers from 2 to any given number:
Sum = n * (n + 1) * 5
Where n is the number of terms in the sequence.
In our case, we had 50 terms (from 2 to 100), so:
Sum = 50 * (50 + 1) * 5 = 550
This formula allows us to quickly calculate the sum of consecutive even numbers for any given range.
Conclusion
In this mathematical exploration, we discovered a fascinating pattern when adding consecutive even numbers from 2 to 100. The sum increases by 10 with each additional term, and we can use a simple formula to calculate the sum for any given range. Whether you're a math enthusiast or just curious about patterns, this exercise is a great way to explore the beauty of mathematics.
