Geometric Sequences

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Geometric Sequences

• (day 3)

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Geometric Sequence Objective

• To find a formula for the nth term of a geometric
  sequence
• To find specified terms of geometric sequences

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Geometric Sequences

• Geometric Sequence A sequence in which the
  ratio of every pair of successive terms is
  constant. This constant ratio is called the
  common ratio and is denoted by r.

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Recall r common ratio tn the nth term
of the sequence

• How would you find the tenth term (t10) of the
  sequence 5, 10, 20, 40,
• Find the common ratio r 2
• (look at the number of times the first term is
  multiplied by the common ratio r n-1 times)
• The 10th term is the product of t1 and the 9th
  power of the ratio

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Geometric Sequence
Formula for finding the nth term
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Ex 1 Find a formula for the nth term of the
geometric sequence 81, 54, 36, 24

• Ex 2 Find t7 for the geometric sequence in the
  above example.

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Ex. 3 Find t7 for the geometric sequence in
which t2 24 and t5 3
(use substitution to solve for r)
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Ex. 4 Find t7 for the geometric sequence in
which t2 6 and t5 750

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Geometric Means

• The terms between two given terms of a geometric
  sequence.
• Ex 1, 2, 4, 8, 16

geometric means between 1 and 16
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Geometric mean of two numbers

• Geometric mean of a and b is
• Ex Find the geometric mean of 2 and 18
• Ex Find the geometric mean of -4 and -64

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-16
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Ex. 5 Insert 2 geometric means between

(multiply consecutive terms by 1/3)
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Homework

• Precalculus
• p513 (w) 2 26 even
• p514 (problems) 1 5
• or
• Algebra II
• Worksheet 3 (1-20)

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Application

• Craig took a job with a starting salary of
  60,000. Find his salary during his sixth year
  if he receives annual raises of
• a) 3,000 or b) 5

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Find the number of terms in the geometric
sequence 1, ,512 given r 2.