Concept explainers
(a).
To Find: The common ratio of a given geometric sequence.
(a).
Answer to Problem 16E
The common ratio of the sequence is
Explanation of Solution
Given Information: The given geometric sequence is
Concept Used: The common ratio of a geometric sequence is the ratio of any of its two consecutive terms.
Calculation: The ratio of the second and first terms (or any other consecutive pair) is
Therefore, the common ratio of the sequence is
(b).
To Find: The
(b).
Answer to Problem 16E
The nineth term of the sequence is
Explanation of Solution
Given Information: The first term of the sequence is
Concept Used: Multiply the common ratio
Calculation:
(c).
To Find: The recursive rule to find the
(c).
Answer to Problem 16E
The series can be recursively defined as
Explanation of Solution
Given Information: The sequence is
Concept Used: Each term in a geometric sequence (except the first term) is the product of its preceding term and the common ratio.
Calculation: The first term in the sequence is
The common ratio is
Therefore, the sequence can be defined recursively as
(d).
To Find: The explicit rule to calculate the
(d).
Answer to Problem 16E
The
Explanation of Solution
Given Information: The first term of the given sequence is
Concept Used: The
Calculation: If the
Therefore, the
Chapter 9 Solutions
Calculus: Graphical, Numerical, Algebraic
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