Download Geometric Sequence

Lesson 1.2
Core Focus on
Ratios, Rates and Statistics
Geometric Sequences
Warm-Up
10
8
1. Simplify the ratio and write the ratio as a fraction, with a
colon and using the word “to”.
5
;
4
5 : 4; 5 to 4
2. The Eagles had a win to loss ratio of 1 : 1. Explain the ratio’s
meaning.
For every 1 win the team had 1 loss.
(The same number of wins as losses.)
3. Curt had 6 yellow flowers and 8 pink flowers. Write the ratio
of yellow flowers to total flowers Curt has.
3
;
7
3 : 7; 3 to 7
Lesson 1.2
Geometric Sequences
Recognize and complete geometric
sequences.
Vocabulary
Sequence
An ordered list of numbers.
2
2
2
2
1
2
4
8
16
1st
term
2nd
term
3rd
term
4th
term
5th
term
Term
A number in a sequence.
Geometric Sequence
A list of numbers created by multiplying the previous term in the sequence by
a common ratio.
Good to Know!
The number you multiply by each time to get the next term is the ratio
between the terms. The ratio can also be determined by writing the ratio
of each term to its previous term.
Example 1
Find the ratio of each geometric sequence. Use the ratio to find the
next two terms of the geometric sequence.
a. 1, 3, 9, 27, …
The find the ratio, divide one term by
the previous term.
3
3
1
9
27
3
3
3
9
The ratio is 3.
Find the next two terms by multiplying
the previous term by 3.
The next two terms are 81 and 243.
27  3 = 81
81  3 = 243
Example 1 Continued…
Find the ratio of each geometric sequence. Use the ratio to find the
next two terms of the geometric sequence.
b. 256, 64, 16, 4, …
The find the ratio, divide one term by
the previous term.
64 1

256 4
16 1

64 4
1
4 1
4
1 1
1 
4 4
1
The ratio is .
4
Find the next two terms by multiplying
the previous term by 1 .
4
1
The next two terms are 1 and .
4
4 1

16 4
Example 2
One geometric sequence begins with the number 2. Another begins
with the number 3. Each geometric sequence has a ratio of 5. Write
the first five terms of each geometric sequence.
Since the ratio of both geometric sequences is 5, multiply each term
in the sequence by 5 to get the next term.
The geometric sequences are:
5 5 5
5
2, 10, 50, 250, 1250, …
5 5 5
and
5
3, 15, 75, 375, 1875, …
Explore!
Number Patterns
Step 1 Find the next two numbers in each sequence (A–E) above.
Step 2 Explain how you found the next two numbers in each sequence.
Step 3 a.
Identify which sequences (A–E) are geometric sequences.
b.
Find the first term of each geometric sequence.
c.
Find the ratio of each geometric sequence.
Step 4 An arithmetic sequence is formed when the same number is added to a term to
find the next term.
a.
Which sequences (A–E) are arithmetic sequences?
b.
Do arithmetic sequences have the same ratio between terms? Explain
using examples.
Step 5 Write the first five terms of your own geometric sequence. Identify the first
term and the ratio of the sequence.
Communication Prompt
How can you identify a geometric sequence if you are
given a list of numbers?
Exit Problems
1. Find the ratio of the geometric sequence
3, 6, 12, 24, 48, …
2
2. Write the first four terms of a geometric sequence with a first
1
term of 81 and a ratio of 3 .
81, 27, 9, 3
3. Determine whether or not the sequence given is a geometric
sequence. Explain your answer.
4, 8, 12, 16, 20, …
Not geometric because
and 12  3 .
8
8
4
2
2
These ratios are not equal.