
arithmetic series


The indicated sum of all terms in an arithmetic sequence. One such example is:
1 + 2 + 3 + . . . + 100 The general formula for an arithmetic series is: S_{n}  = a_{1} + a_{2} + a_{3} + . . . + a_{n}   = a_{1} + (a_{1} + d) + (a_{1} + 2d) + . . . + [a_{1}+(n1)d]   = n(a_{1} + a_{n})/2   = n[2a_{1} +(n1)d]/2 
In the example, the first term, a_{1}, is 1, and the last term, a_{100}, is 100. Using the formula, the sum = 100(1+100)/2 = 5050.

