Question

Kelly cannot remember the formula for the sum of a finite arithmetic sequence, so she is going to try to derive it. Her problem is to find the sum of the numbers 1 to 500. What should she do first?

Answer 1

add forwards and backwards
\(S=1+2+3+...+498+499+500\)
\(S=500+499+498+...+3+2+1\) add together to get
\[2S=501+501+501+...+501+501+501=500\times 501\]

Answer 2

Thanks!!