10.4 Geometric Sequences and Series
KPIs
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10.4 Geometric Sequences and Series
STARTER
Solve the equations:(No decimal approximation. Give exact answers.)
1 x5 = 2
2 x 5 = 243a 10
3
64x 7 =
1
2
4 5x = 2
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10.4 Geometric Sequences and Series
NOTES
10.4.1 Find the common ratio in a geometric sequence given either two
consecutive terms, two nonconsecutive terms, or the equation of the nth
term
1.
Find the common ratio given two consecutive terms of a geometric sequence:
Two consecutive terms of a sequence are represented as:
The common ratio “r” can be found by using :
Examples:
a) Find the common ratio of the geometric sequence if 5 and 15 are two consecutive
terms of the sequence.
b) The third term of a geometric sequence is -30, and the fourth term is 5. What is the
common ratio?
c) If the eleventh term and the twelfth term of a geometric sequence are -3 and 27
respectively, what is the common ratio?
d) In a geometric sequence, a19
= 72 and a20 = 36. What is the common ratio?
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10.4 Geometric Sequences and Series
NOTES
10.4.1 Find the common ratio in a geometric sequence given either two
consecutive terms, two nonconsecutive terms, or the equation of the nth
term
2.
Find the common ratio given two non-consecutive terms of an geometric
sequence:
Two non-consecutive terms of a sequence are represented as:
The common ratio can be found by using :
Examples:
a) The rst term of a geometric sequence is 7, and the fth term is 112. Determine the
common ratio.
b) The second term of a geometric sequence is
common ratio?
fi
fi
4
1
, and the seventh term is 8. What is the
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10.4 Geometric Sequences and Series
NOTES
10.4.1 Find the common ratio in a geometric sequence given either two
consecutive terms, two nonconsecutive terms, or the equation of the nth
term
3.
Find the common ratio given the equation of the nth term:
The nth term of an geometric sequence is of the form:
The common ratio can be found by using :
Step 1: Find ______
Step 2: Find ______
Step 3: Then r = ______
a)
In a geometric sequence, the equation of the nth term is given by an
What is the common ratio?
b) The nth term of a geometric sequence is given by an
= 3(4)n−1.
= 52n−1. Find the common ratio.
2n
c) If the equation of the nth term of a geometric sequence is an =
, what is the
3n−1
common ratio?
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10.4 Geometric Sequences and Series
NOTES
10.4.2 Write the equation of the nth term of an geometric sequence given
a list of consecutive terms or a term and the common ratio
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10.4 Geometric Sequences and Series
NOTES
10.4.3 Find the value of a specific nth term of an geometric sequence
given a list of consecutive terms or a term and the common ratio
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10.4 Geometric Sequences and Series
NOTES
10.4.4 List the geometric means of an geometric sequence between two
given terms
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10.4 Geometric Sequences and Series
NOTES
10.4.5 Identify the geometric series
Recall Series:
Write 3 examples of geometric sequences and the corresponding series for
each sequence in the table below. Also write the indicated Partial Sum.
Sequence
Series
Partial Sum
S3 =
1
2
S5 =
3
S1
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10.4 Geometric Sequences and Series
NOTES
10.4.6 Find the partial sum of a geometric series (Sn) given either the
initial term and the nth term or the initial term and the number of terms
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10.4 Geometric Sequences and Series
NOTES
10.4.7 Apply sigma notation to find the sum of a geometric series
Find the first term a1 =
The common ratio, r =
The number of terms in series, n =
Sn =
Find each sum.
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10.4 Geometric Sequences and Series
NOTES
10.4.8 Find missing terms in a geometric series given a combination of
the sum, first term, nth term, the common ratio and the number of terms
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10.4 Geometric Sequences and Series
NOTES
10.4.9 Solve real world applications related to finite geometric series and
their sums
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10.3 Geometric Sequences and Series PRACTICE
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10.3 Geometric Sequences and Series PRACTICE
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10.3 Geometric Sequences and Series PRACTICE
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