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

9.3 Geometric Sequences and Series


Common ratio

Common Ratio

In the sequence

2, 10, 50, 250, 1250, …..

Find the common ratio


Rule of geometric sequences

Rule of Geometric Sequences

Let a1 = 2

r = 5

Find a6


Rule of geometric sequences1

Rule of Geometric Sequences

Let a2 = 12

a3 = 36

Find a6


Rule of geometric sequences2

Rule of Geometric Sequences

Let a2 = 12

a3 = 36

r = 3

Find a6


Finite sum

Finite Sum

The equation to find the Finite Sum of a Geometric Sequence


Finite sum1

Finite Sum

Let a1 = 7, r = 3.

Find the sum of the first 9 terms


Finite sum2

Finite Sum

Let a1 = 7, r = 3.

Find the sum of the first 9 terms


How many terms

How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio


How many terms1

How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio 3


How many terms2

How many terms

0.25 + 0.75 + 2.25 + …….. = 820

Common ratio 3


Infinite geometric series

Infinite Geometric Series

If |r| < 1, it works


Infinite geometric series1

Infinite Geometric Series

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


Homework

Homework

Page 640 – 641

# 5, 15, 25, 35,

45, 55, 65, 75,

85, 105, 115


Homework1

Homework

Page 640 – 641

# 3, 9, 27, 81, 113


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