Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
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10-7<br />
NAME ______________________________________________ DATE ____________ PERIOD _____<br />
<strong>Study</strong> <strong>Guide</strong> <strong>and</strong> <strong>Intervention</strong><br />
Geometric Sequences<br />
Geometric Sequences A geometric sequence is a sequence in which each term after<br />
the nonzero first term is found by multiplying the previous term by a constant called the<br />
common ratio.<br />
Geometric a sequence of numbers of the form a, ar, ar 2 , ar 3 , …, Example: 1, 2, 4, 8, 16, …<br />
Sequence where a 0, <strong>and</strong> r 0 or 1<br />
Example 1<br />
Exercises<br />
Determine whether each sequence is geometric.<br />
a. 3, 6, 9, 12, 15, …<br />
In this sequence, each term is found by<br />
adding 3 to the previous term. The<br />
sequence is arithmetic <strong>and</strong> not geometric.<br />
224(2) 448<br />
The next three terms are 112, 224, 448.<br />
Determine whether each sequence is geometric.<br />
b. 1, 4, 16, 64, …<br />
In this sequence, each term is found by<br />
multiplying the previous term by 4. The<br />
sequence is geometric.<br />
Example 2<br />
a. 8, 4, 2, 1, …<br />
The common factor is or . Use this<br />
information to find the next three terms.<br />
(1) <br />
<br />
<br />
The next three terms are , , <strong>and</strong> .<br />
1<br />
Find the next three terms in each geometric sequence.<br />
b. 7, 14, 28, 56, …<br />
4 1<br />
<br />
8 2<br />
14<br />
The common ratio is or 2. Use this<br />
7<br />
information to find the next three terms.<br />
1 1<br />
<br />
2 2<br />
56(2) 112<br />
112(2) 224<br />
1 1 1<br />
<br />
2 2 4<br />
1 1 1<br />
<br />
4 2 8<br />
1 1<br />
<br />
2 4 8<br />
224(2) 448<br />
The next three terms are 112, 224, 448.<br />
1. 2, 4, 6, 8, 10, … 2. 2, 4, 8, 16, 32, … 3. 10, 5, 2.5, 1.25, …<br />
1 1 1 1<br />
1 1 1 1<br />
4. 100, 400, 1600, 6400, … 5. , , , , … 6. , , , , …<br />
2 3 4 5<br />
3 9 27 81<br />
Find the next three terms in each geometric sequence.<br />
7. 100, 300, 900, 2700, …<br />
1 1 1 1<br />
8. , , , , …<br />
2 4 8 16<br />
9. 80, 40, 20, 10, …<br />
© Glencoe/McGraw-Hill 615 Glencoe Algebra 1<br />
Lesson 10-7
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