1. 12.2: Arithmetic Sequences
Worksheet Key
17)`
1010
18)
6950
19)
9925
20)
3080
21) 63
22)
-1435
23)
10875
24)
-4750
25) 7
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12.2: Arithmetic Sequences

2. Geometric Sequences & Series
Section 12.5
Pre–Calculus, Revised ©2015
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12.1: Sequences

3. Definitions
Geometric Sequence is where consecutive terms have a common ratio
Geometric Series is indicated sum of the terms of a geometric sequence
Ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another
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12.1: Sequences

4. Is it Geometric? YES r = 3 NO YES r = 0.2
Determine whether these sequences are geometric. If it is, determine the ratio.
1, 3, 9, 27, 81...
180, 90, 60, 15,
5, 1, 0.2, 0.04,
–50, –32, –18, –8, –2 ...
YES r = 3 NO
YES r = 0.2
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12.1: Sequences

5. Steps Find the common ratio Use the formula and determine the rule
Evaluate for the missing variable
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12.1: Sequences

6. Example 1
For this geometric sequence, determine the first four terms of 𝒂 𝒏 =𝟓 𝟐 𝒏−𝟏 n
5(2)n–1 an 1 2 3 4 1
5(2)1–1 5 2
5(2)2–1 10 3
5(2)3–1 20 4
5(2)4–1 40
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12.1: Sequences

7. Example 2
For this geometric sequence, determine the first four terms of 𝒂 𝒏 =𝟓 𝟏 𝟖 𝒏−𝟏
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12.1: Sequences

8. Example 3
Find the 7th term of this geometric sequence of 1, 3, 9, 27, and the explicit rule n an 1 2 3 9 4 27 5 81
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12.1: Sequences

9. Your Turn
Find the 8th term of this geometric sequence of 16, –8, 4, –2, .... and the explicit rule
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12.1: Sequences

10. Example 4
Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324.
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12.1: Sequences

11. Example 4
Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324.
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12.1: Sequences

12. Your Turn
Find the 8th term of the geometric sequence with a2 = 80 and a4 = 1280
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12.1: Sequences

13. Geometric Series
Identify the number of terms, lower and upper limit, and common ratio of the summation
Then, identify the missing terms by plugging the given equation
Apply the geometric summation notation equation, 𝒌=𝟏 𝒏 𝒂 𝒌 𝒓 𝒏 = 𝒂 𝟏 𝟏− 𝒓 𝒏 𝟏−𝒓 where ak is the given equation, a1 is the given term, and an is the last term
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12.1: Sequences

14. Example 5
Find the indicated sum for the geometric series of s8 = …
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12.1: Sequences

15. Example 6
Evaluate 𝒌=𝟏 𝟏𝟎 𝟐 𝒌
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12.1: Sequences

16. Your Turn
Find the indicated sum for the geometric series of s9 = –3 + –6 + –12…
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12.1: Sequences