SOLUTION: I need to find the sum of 2+4+6+8+10+...+1020. I know I'm adding 2 to each number but I can't figure out how to sum them all. Please help. Thank you.

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Question 414395: I need to find the sum of 2+4+6+8+10+...+1020.
I know I'm adding 2 to each number but I can't figure out how to sum them all.
Please help. Thank you.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
{2,4,6,8,10,...,1020} is an Arithmetic Sequence where difference between the terms = 2
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad
1020=2+(n-1)*2
1018/2 = n-1
509 + 1 = n
510 = n (1020 is the 510 term) Note: 1020/2 = 510
S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29
S%5B510%5D=%28510%2F2%29%282%2A2%2B+%28509%292%29 = 255(1022) = 260,610