1. Chapter 8: Sequences and Series Lesson 4: Geometric Series Mrs. Parziale

2. Vocabulary: Geometric Series: is an indicated sum of terms of a geometric sequence. – Example – add the first 5 terms in this sequence 1, 2, 4, 8, 16, … nth partial sum: is the sum S n of the first n terms in a sequence S n = 1+2+4+8+16 = 31

3. Example 1: Consider the sequence 3 1 + 3 2 + 3 3 + 3 4 + 3 5 Find This is a finite geometric series s n = g 1 + g 2 + g 3 + g 4 + g 5 The sum of a finite geometric series with first term g 1 and a constant ratio of r is given by:

4. Example 1, cont.: First, add 3 1 + 3 2 + 3 3 + 3 4 + 3 5 = _______ Now use the formula to find :

5. Example 2: Find

6. Example 3: You have 2 children, each of them have 2 kids, etc. How many generations until you have 1000 descendants?

7. Closure Find the sum of the first ten terms in the geometric series: -3, 9, -27, 81, … Find the sum for the following: