Question

What is the sum of all even numbers between 1 and 1000

Answer 1

There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,

                                       S = (a1 + an)(n/2)
and substituting, 
                                     
                                        S = (2 + 998)(500/2)
we get, 

                                        S = 250,000

Therefore, the sum of all even numbers between 1 and 1000 is 250,000.