Geometric Sequences as Exponential Functions

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Presentation transcript:

Geometric Sequences as Exponential Functions Chapter 7.7 Geometric Sequences as Exponential Functions

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. 0 8 16 24 32 8 – 0 = 8 16 – 8 = 8 24 – 16 = 8 32 – 24 = 8

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 64 48 36 27 __ 3 4 ___ 48 64 = __ 3 4 ___ 36 48 = __ 3 4 ___ 27 36 =

Memorize… Common Difference SUBTRACTION Common Ratio MULTIPLICATION Arithmetic Sequence Geometric Sequences Common Difference SUBTRACTION Common Ratio MULTIPLICATION

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

Your Turn… Find the next three terms in the geometric sequence. 1, –8, 64, –512, ...

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!

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

Homework 15-31 odd