Chapter 7.7 Geometric Sequences as Exponential Functions.
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Chapter 7.7 Geometric Sequences as Exponential Functions
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Transcript of Chapter 7.7 Geometric Sequences as Exponential Functions.
Chapter 7.7Geometric 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:
64 48 36 27
__34
___4864
=__34
___3648
=__34
___2736
=
Common Ratio
Memorize…
Arithmetic Sequence
Common Difference SUBTRACTION
Geometric Sequences
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
Homework15-31 odd
