1. Objectives:
1. Find the sum of the first n terms of
arithmetic or geometric series

2. What is a Series?
The sum of the terms of a sequence.
Finite sequence: 2, 6, 10, 14
Finite series: 2 + 6 + 10 + 14
Infinite sequence:
Infinite series:

3. Notation
Sn represents the sum of n terms of
a series.
Explicit definition of Sn
Sn = t1 + t2 + t3 + … + tn

4. Finite Arithmetic Series
The sum of the first n terms of an
arithmetic series is:
(The number of terms times the avg.
of the first and last terms.)

5. Example 1
Find the sum of the cubes of the first
20 positive integers.

6. Example 2
Find the sum of the first 25 terms of
the series 11 + 14 + 17 + 20 + …

7. You Try!
Find the sum of the series:
3 + 7 + 11 + … + 99

8. Finite Geometric Series
The sum of the first n terms of a
geometric series is:

9. Example
Find the sum of the first 10 terms of
2 – 6 + 18 – 54 + ….

10. You Try!
Find the sum of
3 + 9 + 27 + … + 6561