Geometric Sequences

1
Geometric Sequences

• PMa 12
• Mr. C. Hunter

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Describe the pattern. State the next term.
a) 2, 10, 50, 1250
b) 48, 24, 12, 6
c) 3, 9, 15, 21
d) 5, -20, 80, -320
e) 2, 5, 10, 17
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Which of the following are geometric sequences?
a) 2, 10, 50, 1250
r 5
b) 48, 24, 12, 6
r ½
c) 3, 9, 15, 21
d) 5, -20, 80, -320
r - 4
e) 2, 5, 10, 17
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Consider the first example. Look for a pattern.
2(5)9
2(5)99
2(5)n-1
5
This leads to the formula
tn arn-1
a is the first term, r is the common ratio, and
n is the number of terms
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1. Find the indicated term of each geometric
sequence.
a) 5, 15, 45, . . . Find t8.
a 5, r 3, n 8 Note
Therefore, t8 5(3)7
t8 10 935
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b) 24, -12, 6, . . . Find t11.
a 24, r -½, n 11 Note
Therefore, t11 24(-½)10
8
c) 9, 12, 16, . . . Find t7.
a 9, r 4/3, n 7 Note
Therefore,
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2. Use the given two terms of a geometric
sequence to find the indicated term.
a) t3 18, t7 1458 Find t10.
Divide the equations
as cancel, subtract exponents
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solve for r
substitution
solve for a
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2. Use the given two terms of a geometric
sequence to find the indicated term.
b) t5 36, t8 288 Find t12.
Divide the equations
as cancel, subtract exponents
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solve for r
substitution
solve for a
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3. Amardeep buys a car for 20 000. It
depreciates at 15/a.
a) Find its value 5 years from now.
As an exponential function,
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As a geometric sequence,
1
2
3
4
5
6
The 5th year is actually the 6th term (We start
counting from year 0)
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b) Amardeep later sells his car for 2500. How
old is the car?
Solve the exponential equation
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c) Seven years from, Amardeep sells his car for
6000. Find the depreciation rate.
t 7 years (8th term)
The depreciation rate is 16
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