# 9.3 Geometric Sequences and Series - PowerPoint PPT Presentation

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9.3 Geometric Sequences and Series. Common Ratio. In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio. Rule of Geometric Sequences. Let a 1 = 2 r = 5 Find a 6. Rule of Geometric Sequences. Let a 2 = 12 a 3 = 36 Find a 6. Rule of Geometric Sequences.

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9.3 Geometric Sequences and Series

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## 9.3 Geometric Sequences and Series

### Common Ratio

In the sequence

2, 10, 50, 250, 1250, …..

Find the common ratio

Let a1 = 2

r = 5

Find a6

Let a2 = 12

a3 = 36

Find a6

Let a2 = 12

a3 = 36

r = 3

Find a6

### Finite Sum

The equation to find the Finite Sum of a Geometric Sequence

### Finite Sum

Let a1 = 7, r = 3.

Find the sum of the first 9 terms

### Finite Sum

Let a1 = 7, r = 3.

Find the sum of the first 9 terms

### How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio

### How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio 3

### How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio 3

### Infinite Geometric Series

If |r| < 1, it works

### Infinite Geometric Series

Since |0.2| < 1, it works. Let a1 = 42

Page 640 – 641

# 5, 15, 25, 35,

45, 55, 65, 75,

85, 105, 115

### Homework

Page 640 – 641

# 3, 9, 27, 81, 113