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**Geometric Sequences as Exponential Functions**

Chapter 7.7 Geometric Sequences as Exponential Functions

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**Review… Arithmetic Sequences**

If a sequence of numbers has a common difference (SUBTRACTION), then the sequence is said to be arithmetic. Example: The common difference for this sequence is 8. 8 – 0 = 8 16 – 8 = 8 24 – 16 = 8 32 – 24 = 8

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**Geometric Sequences… The Basics**

In a geometric sequence, the first term is a nonzero. Each term after the first can be found by MULTIPLYING the previous term by a constant (r) known as the common ratio. Example: Common Ratio __ 3 4 ___ 48 64 = __ 3 4 ___ 36 48 = __ 3 4 ___ 27 36 =

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**Memorize… Common Difference SUBTRACTION Common Ratio MULTIPLICATION**

Arithmetic Sequence Geometric Sequences Common Difference SUBTRACTION Common Ratio MULTIPLICATION

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Your Turn… Determine whether the sequence is arithmetic, geometric, or neither. A. 1, 7, 49, 343, ... B. 1, 2, 4, 14, 54, ...

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**Your Turn… Find the next three terms in the geometric sequence.**

1, –8, 64, –512, ...

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**nth term of a Geometric Sequence…**

Write an equation for the nth term of the geometric sequence 1, –2, 4, –8, ... a1 = Common Ratio = Now, plug into the formula!

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**Finding a specific nth term…**

Find the 12th term of the sequence. 1, –2, 4, –8, ... Find the 7th term of this sequence using the equation an = 3(–4)n – 1

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Homework 15-31 odd

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