# Lesson 6-2 - Get as PowerPoint

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5-Minute Check on Chapter 2
1. Evaluate 42 - |x - 7| if x = -3

2. Find 4.1  (-0.5)

Simplify each expression

3. 8(-2c + 5) + 9c                                  4. (36d – 18) / (-9)

5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops.
If one is chosen at random, what is the probability that it is
not green?

6.   Standardized Test Practice:   Which of the following is a true
statement
A   8/4 < 4/8       B    -4/8 < -8/4         C       -4/8 > -8/4   D   -4/8 > 4/8
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Lesson 10-7

Geometric Sequences
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Objectives
• Recognize and extend geometric sequences

• Find geometric means
Vocabulary

• Geometric sequence –

• Common ratio –

• Geometric means –
Four Step Problem Solving Plan
• Step 1: Explore the Problem
– Identify what information is given (the facts)
– Identify what you are asked to find (the question)
• Step 2: Plan the Solution
– Find an equation the represents the problem
– Let a variable represent what you are looking for
• Step 3: Solve the Problem
– Plug into your equation and solve for the variable
• Step 4: Examine the Solution
– Does it fit the facts in the problem?
Example 1a
A. Determine whether the sequence is geometric.
1, 4, 16, 64, 256, …
Determine the pattern.
1     4      16        64    256

In this sequence, each term in found by multiplying the
previous term by 4.
Example 1b

B. Determine whether the sequence is geometric.
1, 3, 5, 7, 9, 11, …

Determine the pattern.
1     3       5        7       9      11

In this sequence, each term is found by adding 2 to the
previous term.
Answer: This sequence is arithmetic, not geometric.
Example 2a

Find the next three terms in the geometric sequence.
20, –28, 39.2, …

Divide the second term by the first.

The common factor is –1.4. Use this information to find the
next three terms.
20, –28, 39.2     –54.88      76.832 –107.5648

Answer: The next 3 terms are –54.88, 76.832, and –107.5648.
Example 2b
Find the next three terms in the geometric sequence.
64, 48, 36, …

Divide the second term by the first.

The common factor is 0.8. Use this information to find the
next three terms.
64, 48, 36        27        20.25      15.1875

Answer: The next three terms are 27, 20.25, and 15.1875.
Example 3
Geography The population of the African country of Liberia
was about 2,900,000 in 1999. If the population grows at a
rate of about 5% per year, what will the population be in the
years 2003, 2004, and 2005?
Year                   Population
The population       1999                    2,900,000
is a geometric       2000           2,900,000(1.05) or 3,045,000
sequence. The        2001           3,045,000(1.05) or 3,197,250
first term is        2002          3,197,250(1.05) or 3,357,112.5
2,900,000 and
2003         3,357,112.5(1.05) or 3,524,968.1
the common
ratio is 1.05.       2004         3,524,968.1(1.05) or 3,701,216.5
2005         3,701,216.5(1.05) or 3,886,277.3
Answer: The population of Liberia in the years 2003, 2004, and
2005 will be about 3,524,968, 3,701,217, and 3,886,277,
respectively.
Example 4
Find the eighth term of a geometric sequence in
which

Formula for the nth term of
a geometric sequence

Answer: The eighth term in the sequence is 15,309.
Example 5
Find the geometric mean in the sequence 7, ___, 112.
In the sequence,            and               To find
you must first find r.
Formula: nth term of a geometric sequence

Divide each side by 7.

Simplify.
Take the square root of each side.
If r = 4, the geometric mean is 7(4) or 28.
If r = -4, the geometric mean is 7(–4) or –28.

Answer: The geometric mean is 28 or –28.
Example 5, alternate way
Find the geometric mean in the sequence 7, ___, 112.

The geometric mean (GM) of two numbers, a and b,
is the square root of their product: GM = ab.

The geometric mean in the sequence, 7, ___, 112 would
be (the number between them)

GM = 7112 = 784 =  28.

Check: (using r from last page) 74 = 28 and 284 = 112
Summary & Homework

• Summary:
– A geometric sequence is a sequence in which
each term after the nonzero first term is found by
multiplying the previous term by a constant
called the common ratio r, where r ≠ 0 or 1
– The nth term an of a geometric sequence with
the first term a1 and a common ratio r is given by
an = a1r n-1

• Homework:
– none

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