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

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Presentation transcript:

Warm Up Find the geometric mean of 49 and 81.

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

Series Introduction Here are examples of Sequence: 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/Progression Formula: 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/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 2.01 + 2.02 + 2.03 + … + 3.00 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.