💯 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? Verified
Zhen HuaExperienced GCSE Maths&Biology Tutor88 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!  