Download 11-3 Geometric Sequences

11-3 Geometric Sequences
Concept #1 Identifying a Geometric Sequence
A geometric sequence is a sequence where the ratio between consecutive
terms is constant. The ratio is call the common ratio.
Is the given sequence geometric? If so, identify the common ratio and the
next two terms.
Ex. 2 15, 30, 45, 60, ...
Ex. 1 5, 15, 45, 135, ...
Ex. 4 10, 4, 1.6, .64, ...
Ex. 3 18, -6, 2, -2/3, ...
Concept #2 Writing Formulas for Geometric Sequences
Recursive Formula
an = an-1 * r
an is the nth term
Explicit Formula
an = a1 * rn-1
n is the number of the term
r is the common ratio
Write the explicit formula for each sequence. Then generate the first five
terms.
Ex. 5 a1 = 5 r = -3
Ex. 6 a1 = 1/2 r = 2/3
Ex. 7 a1 = 100 r = -20
Ex. 8 a1 = 1024 r = .5
Concept # 3 Using the Geometric Mean
Geometric Mean = √(product of two given numbers)
Ex. 9 3, __, .75, ...
Ex. 10 12, __, 3, ...
Ex. 11 12.5, __, __, __, 5.12, ...
Ex. 12 19,683, __, __, __, 243, ...
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Mar 19­8:26 AM
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