Evaluate 21+27+33+...+999.

http://www.wolframalpha.com/input/?i=%E2%88%91%5B21%2B6n%5D,+n%3D0+to+163

=83,640

 21+27+33+...+999 → 15 + 6*(1 + 2 + 3 + ... + 164)  →  15+6*164*(164+1)/2 →  81195

.

21+27+33+999=1,080

The number of terms, n   = [999 - 21] / 6 + 1  = 164

And the sum is given by :

(n /2) (a₁ + a₁₆₄)         where a₁ = 21 and a₁₆₄ = 999

(164)/2  *  (21 + 999)  =  83,640