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Algebra 2: Lesson 11-2 Arithmetic and Geometric Sequences
Learning Goals:
1. What is an arithmetic sequence? What is the common difference of an arithmetic sequence?
2. How can we find the nth term of an arithmetic sequence?
3. What is a geometric sequence? What is the common ratio of a geometric sequence?
4. How can we find the nth term of a geometric sequence?
Arithmetic Sequence:
Common Difference:
Geometric Sequence:
Common Ratio:
Practice:
1) Is the following sequence arithmetic?
32, 27, 21, 17, 10,…
2) Is the following sequence geometric?
512, 128, 64, 8, …
3) Write a rule for the nth term of the arithmetic sequence. Then find a22.
9, 5, 1, -3,…
4) Write a rule for the nth term of the geometric sequence. Then find a9.
14, 28, 56, 112, …
5) Write a rule for the nth term of the arithmetic
sequence.
a15 = 107, d = 12
6) Write a rule for the nth term of the geometric
sequence.
a5 = 324, r = -3
7) If a geometric sequence has a1 = 256 and a8 = 512, find the exact value of the common ratio r.
8) Given the geometric sequence defined by the following values of a 1 and r, find the value of n so that
an has the specified value.
a1 = 64,
an=2