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:
|Sn|| = a1 + a2 + a3 + . . . + an|
| = a1 + (a1 + d) + (a1 + 2d) + . . . + [a1+(n-1)d]|
| = n(a1 + an)/2|
| = n[2a1 +(n-1)d]/2|
In the example, the first term, a1, is 1, and the last term, a100, is 100. Using the formula, the sum = 100(1+100)/2 = 5050.