1. Warm Up
Find the geometric mean of 49 and 81.

2. Today’s Objectives: Differentiate between a sequence and a series
Find the sum of the first n terms of an arithmetic series

3. Series Introduction Here are examples of Sequence: Series:
–5, –1, 3, 7, 11, … –5 – …
1. What is the difference between a sequence and a series? (Use this to define what is a series)
2. Find the sum of the first 4 terms.

4. Sum of an Arithmetic Series/Progression
Formula: Sn = sum of the first n terms
n = number of terms
A1 = 1st term
An = nth term OR

5. Examples:
1. The first term of an arithmetic series is 2 and the last term is 46. If the series has 23 terms, find the sum of all the terms.

6. Examples: 2. Find the sum of the first sixteen terms of the AP…

7. Classwork/Homework Find the number of terms in the sequence
6.25, 7.5, 8.75, …, 31.25
The first term of an AP is 2 and the common difference is 5. If the sum of the terms is 245, how many terms does the series have?
Find the sum of the following AP
-10 – 7 – 4 – … + 50 …
The first term of an AP is 13 and the fifth term is 21. Find the common difference and the sum of the first 10 terms.