arithmetic series
The indicated sum of all terms in an arithmetic sequence. One such example is:

symbol space1 + 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.

Related Terms: geometric series, sequence (progression), series


 
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