Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3....
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Transcript of Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3....
![Page 1: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/1.jpg)
Holt Algebra 1
11-1Geometric Sequences
Warm UpFind the value of each expression.
1. 25 2. 2–5
3. –34 4. (–3)4
32
5. (0.2)3 6. 7(–4)2
–81 81
112 0.008
7. 8. 12(–0.4)3 –0.768
![Page 2: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/2.jpg)
Holt Algebra 1
11-1Geometric Sequences
Students will be able to: Recognize and extend geometric sequences and find the nth term of a geometric sequence.
Learning Targets
![Page 3: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/3.jpg)
Holt Algebra 1
11-1Geometric Sequences
The table shows the heights of a bungee jumper’s bounces.
The height of the bounces shown in the table above form a geometric sequence. In a geometric sequence, the ratio of successive terms is the same number r, called the common ratio.
![Page 4: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/4.jpg)
Holt Algebra 1
11-1Geometric SequencesExample 1A: Extending Geometric Sequences
Find the next three terms in the geometric sequence.
1, 4, 16, 64,…
5, –10, 20,–40,… 512, 384, 288,…
![Page 5: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/5.jpg)
Holt Algebra 1
11-1Geometric Sequences
When the terms in a geometric sequence alternate between positive and negative, the value of r is negative.
Helpful Hint
The variable a is often used to represent terms in a sequence. The variable a4 (read “a sub 4”)is the fourth term in a sequence.
Writing Math
![Page 6: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/6.jpg)
Holt Algebra 1
11-1Geometric Sequences
The variable a is often used to represent terms in a sequence. The variable a4 (read “a sub 4”)is the fourth term in a sequence.
Writing Math
![Page 7: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/7.jpg)
Holt Algebra 1
11-1Geometric SequencesGeometric sequences can be thought of as functions. The term number, or position in the sequence, is the input of the function, and the term itself is the output of the function.
a1 a2 a3 a4
1 2 3 4 Position
3 6 12 24 Term
To find the output an of a geometric sequence when n is a large number, you need an equation, or function rule. Look for a pattern to find a function rule for the sequence above.
![Page 8: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/8.jpg)
Holt Algebra 1
11-1Geometric Sequences
The pattern in the table shows that to get the nth term, multiply the first term by the common ratio raised to the power n – 1.
![Page 9: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/9.jpg)
Holt Algebra 1
11-1Geometric Sequences
If the first term of a geometric sequence is a1, the nth term is an , and the common ratio is r, then
an = a1rn–1
nth term 1st term Common ratio
![Page 10: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/10.jpg)
Holt Algebra 1
11-1Geometric SequencesThe first term of a geometric sequence is 500, and the common ratio is 0.2. What is the 7th term of the sequence?
For a geometric sequence, a1 = 5, and r = 2. Find the 6th term of the sequence?
What is the 9th term of the geometric sequence 2, –6, 18, –54, …?
![Page 11: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/11.jpg)
Holt Algebra 1
11-1Geometric Sequences
When writing a function rule for a sequence with a negative common ratio, remember to enclose r in parentheses. –212 ≠ (–2)12
Caution
![Page 12: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/12.jpg)
Holt Algebra 1
11-1Geometric SequencesWhat is the 8th term of the sequence 1000, 500, 250, 125, …?
![Page 13: Holt Algebra 1 11-1 Geometric Sequences Warm Up Find the value of each expression. 1. 2 5 2. 2 5 3. 3 4 4. (3) 4 32 5. (0.2) 3 6. 7(4) 2 81 81 112.](https://reader036.fdocuments.net/reader036/viewer/2022082601/5a4d1b6f7f8b9ab0599b4dba/html5/thumbnails/13.jpg)
Holt Algebra 1
11-1Geometric SequencesA ball is dropped from a tower. The table shows the heights of the balls bounces, which form a geometric sequence. What is the height of the 6th bounce?
Bounce Height (cm)
1 3002 1503 75
HW pp. 769-771/8-40,42-46,54-62