The Formula for the Sum of Consecutive Numbers
Have you ever wondered how to calculate the sum of consecutive numbers from 1 to 100? Well, you're in luck because today we're going to explore the formula behind this calculation.
What is the Formula?
The formula for the sum of consecutive numbers is given by:
1 + 2 + 3 + ... + n = n(n+1)/2
Where n is the last number in the sequence.
How Does it Work?
Let's break down the formula to understand how it works.
- The formula is based on the concept of an arithmetic series, where each term is obtained by adding a fixed constant to the previous term.
- The n in the formula represents the last number in the sequence.
- The (n+1)/2 part of the formula calculates the average of the sequence.
- Multiplying n by the average gives us the sum of the sequence.
Example: Calculating the Sum of 1 to 100
Using the formula, let's calculate the sum of consecutive numbers from 1 to 100.
1 + 2 + 3 + ... + 100 = 100(100+1)/2 = 100(101)/2 = 5050
Therefore, the sum of consecutive numbers from 1 to 100 is 5050.
Conclusion
In conclusion, the formula for the sum of consecutive numbers is a powerful tool for quickly calculating the sum of a sequence of numbers. Whether you're a math enthusiast or just need to calculate a quick sum, this formula is sure to come in handy.
So the next time you need to calculate the sum of consecutive numbers, just remember: n(n+1)/2.
