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The sum of an infinite geometric series is three times the first term. Find the common ratio of this series.
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Important Questions on From Patterns to Generalizations: Sequences and Series
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Diploma
IMPORTANT
Create two different infinite geometric series that each have a sum of 8.
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In a geometric sequence, the fourth term is times the first term. The sum of the first terms is . Find the th term of this sequence.
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A large company created a phone tree to contact all employees in case of an emergency. Each of the five vice presidents calls five employees, who in turn each call five other employees, and so on. How many rounds of phone calls are needed to reach all employees?
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Diploma
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A geometric sequence has all positive terms. The sum of the first two terms is and the sum to infinity is . Find the value of the common ratio.
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Diploma
IMPORTANT
A geometric sequence has all positive terms. The sum of the first two terms is and the sum to infinity is . Find the first term.
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IMPORTANT
The first three terms of an infinite geometric sequence are . Write down two expressions for .
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Diploma
IMPORTANT
The first three terms of an infinite geometric sequence are . Find two possible values of .
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Diploma
IMPORTANT
The first three terms of an infinite geometric sequence are . Find two possible values of .
