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Sum of Numbers 1 to 1000: Calculate the Total
Published on October 11, 2024
Pre-Algebra
Find the sum of the first 1000 natural numbers. This math problem can be solved using the formula for arithmetic series, resulting in a sum of 500,500.
Question
1+2+3+4+5....+1000=？
Answer
This is the sum of an arithmetic series. Here’s how to solve it:
Understanding Arithmetic Series
An arithmetic series is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference.
In this case, the series is 1, 2, 3, …, 1000, and the common difference is 1.
Formula
The sum (S) of an arithmetic series is found using the following formula:
S = (n/2) * (a + l)
Where:
- n = number of terms
- a = first term
- l = last term
Applying the Formula
-
Identify n, a, and l:
- n (number of terms) = 1000
- a (first term) = 1
- l (last term) = 1000
-
Substitute the values into the formula:
S = (1000/2) * (1 + 1000) -
Simplify the equation:
S = 500 * 1001 -
Calculate the sum:
S = 500500
Answer: 1 + 2 + 3 + 4 + … + 1000 = 500500