Name ________________________________________ Date __________________ Class __________________
LESSON
10-3
Geometric Sequences
Practice and Problem Solving: D
Evaluate each geometric sequence for n = 4. The first one is done
for you.
1. f(n) = 10(3)n−1
2. f(n) = 2(5)n−1
3
f(4) = 10(3) = 270
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3. f(1) = 4; f(n) = f(n − 1) • 2 for n ≥ 2
4. f(1) = 200; f(n) = f(n − 1) • 0.5 for n ≥ 2
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Each rule represents a geometric sequence. If the given rule
is recursive, write it as an explicit rule. If the rule is explicit, write it
as a recursive rule. Assume that f(1) is the first term of the sequence.
The first one is done for you.
6. f(n) = 16(8)n−1
5. f(1) = 7; f(n) = f(n − 1) • 3 for n ≥ 2
n−1
f(n) = 7(3)
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7. f(n) = 4.5(13)n−1
8. f(1) = 100; f(n) = f(n − 1) • 0.6 for n ≥ 2
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Write an explicit rule for each geometric sequence based on the given
terms from the sequence. Assume that the common ratio r is positive.
The first one is done for you.
9. a1 = 9 and a2 = 18
10. a1 = 2 and a2 = 20
n−1
f(n) = 9(2)
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11. a1 = 5 and a3 = 80
12. a2 = 12 and a3 = 36
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The population of a town is 20,000. It is expected to grow at 4% per
year. Use this information for Problems 13–15. The first one is started
for you.
13. Write a recursive rule and an explicit rule to predict the population,
p(n), n years from today.
p(1) = 20,000; p(n) = f(n − 1) • 1.04 for n ≥ 2
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14. Use a rule to predict the population in 5 years and in 10 years.
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15. Which rule is easier to use for Problem 14? Explain.
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