Formula to Calculate the Sum of Consecutive Numbers: 1+2+3+4+5+6 to 100
The formula to calculate the sum of consecutive numbers, such as 1+2+3+4+5+6 to 100, is a fundamental concept in mathematics. This formula is widely used in various mathematical calculations, including arithmetic progressions.
The Formula:
The formula to calculate the sum of consecutive numbers is:
1 + 2 + 3 + ... + n = n(n+1)/2*
Where n is the last number in the sequence.
How it Works:
To understand how this formula works, let's break it down:
- The sequence of numbers starts from 1 and increments by 1 for each subsequent number (1, 2, 3, ..., n).
- The formula uses the concept of arithmetic progression, where each term is obtained by adding a fixed constant (in this case, 1) to the previous term.
- The formula takes advantage of the fact that the sum of consecutive numbers forms a triangular number.
Example:
Let's calculate the sum of consecutive numbers from 1 to 100:
1 + 2 + 3 + ... + 100 = ?
Using the formula:
n = 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:
The formula to calculate the sum of consecutive numbers is a powerful tool in mathematics. It allows us to quickly and efficiently calculate the sum of a sequence of numbers, making it an essential concept in various mathematical calculations.
