πŸ’― 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?

2 answers
Answered Jan 20Maths
Verified
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!

Answered Feb 19Maths
Verified
Verified
Rima Ranu4 years experience working in primary schools and SATS tutoring.166 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