Get an answer in 5 minutes Ask a question to our educators
MATHS

# Hello, how would I work out the sum of the even numbers between 1 and 1000? Is there an equation I can use? Thanks?

Use Gauss’ formula: sum = 1000/2 *(1000+2) = 250500  Dan Ritchie
·

17k students helped

Hi Rima, I slightly disagree with your answer. Firstly, the formula for sum of natural number is 1/2n(n+1). Secondly, sum of natural number is 1+2+3+4+5+...., the situation here is sum of even number between 1 and 1000, so the summation formula here doesn't really work. There are two methods to do this question: Method 1: this sequence is 2+4+6+....+1000, so it is an arithmetic sequence. The formula for sum of arithmetic sequence is n/2(first number+last number). In this case, there are 500 numbers, so sum is 500/2(2+1000)=250500 Method 2(if you have done A-level further maths): sum of even number is (sum sign)r=1, 500, 2r, then it becomes 2*(sum sign)r=1, 500, r, so you are working out the sum of natural number from 1 to 500 and then time by 2. So it is 2*(1/2)n(n+1). In this case, yes the formula becomes n(n+1) because 2 cancels 1/2, but n(n+1) is not the formula for sum of natural number. The correct formula for sum of natural is 1/2*n*(n+1). I hope you find this answer helpful!  Zhen Hua
·

7.9k students helped

The equation for figuring out the sum of natural numbers is n(n+1). The n stands for how many numbers are actually even within that series of 1-1000. We know that there are 500 numbers that are even between 1-1000 therefore n=500. We can then plug 500 into our equation. 500(500+1) =500 x 501 =250500  Rima Ranu
·

443 students helped

## What is Q&A on Scoodle?

At Scoodle we understand that everyone learns in a different way. Some people learn through practice, using essays and notes; others prefer video lessons to watch and learn, some just need help with a specifically hard question, while some learn best 1-on-1 tutoring sessions. At Scoodle we cater for all types of learning styles and needs. From GCSE Maths video lessons to A-level English essays and specialist educators in every subject - we’ve got you covered.   Scoodle has helped over 131,000 students so far

Need help with Maths?

Getting expert help from a tutor is a great way to improve your Maths grades.

## Discover learning resources by tutors

Learn Maths with Video Lessons