The Sum of Consecutive Numbers: 1+2+3+...+49
The sum of consecutive numbers, also known as an arithmetic series, is a fundamental concept in mathematics. In this article, we will explore the sum of the first 49 consecutive numbers, from 1 to 49.
The Formula
The formula to calculate the sum of an arithmetic series is:
Sn = n/2(2a + (n-1)d)
where:
- Sn is the sum of the series
- n is the number of terms
- a is the first term
- d is the common difference
Calculating the Sum
In our case, we want to calculate the sum of the first 49 consecutive numbers, from 1 to 49. Plugging in the values, we get:
- n = 49
- a = 1
- d = 1 (since each consecutive number increases by 1)
Substituting these values into the formula, we get:
Sn = 49/2(2(1) + (49-1)1) Sn = 49/2(2 + 48) Sn = 49/2(50) Sn = 49(25) Sn = 1225
Therefore, the sum of the first 49 consecutive numbers is 1225.
Conclusion
In conclusion, we have calculated the sum of the first 49 consecutive numbers using the formula for an arithmetic series. This calculation has many real-world applications, from finance to engineering, and is an essential concept in mathematics.
