Warm Up1. Find the geometric mean of 49 and 81.

Today’s Objectives:

1. Differentiate between a sequence and a series

2. Find the sum of the first n terms of an arithmetic series

Series IntroductionHere are examples ofSequence: Series: –5, –1, 3, 7, 11, … –5 – 1 + 3 + 7 + 11 +

…

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.

Sum of an Arithmetic Series/ProgressionFormula: Sn = sum of the first n terms

n = number of terms

A1 = 1st term

An = nth term

OR

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.

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

3 + 10 + 17 + …

Classwork/Homework1. Find the number of terms in the sequence

6.25, 7.5, 8.75, …, 31.252. 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?

3. Find the sum of the following AP1. -10 – 7 – 4 – … + 502. 2.01 + 2.02 + 2.03 + … + 3.00

4. 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.