2. 1.2 Arithmetic Series

Objectives:

  1. Derive a rule for determining the sum of n terms of an arithmetic series.
  2. Determine the first term, the common difference, the number of terms, or the value of the sum of specific numbers of terms in a problem involving an arithmetic series.
  3. Solve a problem that involves an arithmetic sequence or series.

You can think of an Arithmetic Series as the sum of an Arithmetic Sequence.

For example, for the arithmetic sequence 3, 8, 13, 18, 23

the arithmetic series would be 3 + 8 + 13 + 18 + 23

The common difference and general term is the same in the series as it is for the sequence, however, we need a formula for determining the sum of the arithmetic series. Two formulas can be shown to be:

  • Sn = \( \frac{n}{2} \)[2t1 + (n - 1)d]
  • Sn = \( \frac{n}{2} \)(t1 + tn)