Concept Byte: Geometric Sequences

Use With Lesson 7-6

ACTIVITY

Recall that a sequence is a list of numbers that often forms a pattern. Each number in a sequence is a term of the sequence.

In Chapter 4 you studied arithmetic sequences, where you found each new term by adding the same number to the previous term. Another kind of sequence is a geometric sequence. In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.

Activity 1

1. 1. What is the common ratio of the sequence 2, 4, 8, 16, …?
   2. What are the next three terms in the sequence?
2. 1. What is the common ratio of the sequence 80, 20, 5, 5 4 , 5 fourths , comma  …?
   2. What are the next three terms in the sequence?
3. 1. What is the common ratio of the sequence 2 , − 6 , 18 , − 54 , … ? 2 comma negative 6 comma 18 comma negative 54 comma dot dot dot question mark
   2. What are the next three terms in the sequence?

You can use the common ratio of a geometric sequence to write a function rule for the sequence.

Activity 2

Consider the sequence 2, 6, 18, 54, …

Let n = the n equals the  term number in the sequence.

Let A ( n ) = the eh open n close equals the  value of the nth term of the sequence.

4. What is the common ratio of the sequence?

5. Complete each statement.

   1. A ( 1 ) = 2 = 2 · 3   eh open 1 close equals 2 equals 2 middle dot , 3 super begin box , , end box end super
   2. A ( 2 ) = 6 = 2 · 3 = 2 · 3   eh open 2 close equals 6 equals 2 middle dot 3 equals 2 middle dot , 3 super begin box , , end box end super
   3. A ( 3 ) = 18 = 2 · 3 · 3 = 2 · 3   eh open 3 close equals 18 equals 2 middle dot 3 middle dot 3 equals 2 middle dot , 3 super begin box , , end box end super
   4. A ( 4 ) = 54 = 2 · 3 · 3 · 3 = 2 · 3   eh open 4 close equals 54 equals 2 middle dot 3 middle dot 3 middle dot 3 equals 2 middle dot , 3 super begin box , , end box end super
6. What is the relationship between the exponent of the base 3 and the value of n?
7. Complete the statement: A ( n ) = 2 · 3   . eh open n close equals 2 middle dot , 3 super begin box , , end box end super , .

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