Concept explainers
In Problems 1–6, determine if the sequence is arithmetic, geometric, or neither. If arithmetic or geometric, determine the first term and the common difference or common ratio.
1.
Whether the given sequence is arithmetic, geometric or neither and find the first term
Answer to Problem 1PCT
The sequence
Explanation of Solution
Definition used:
Arithmetic:
“If the difference between consecutive terms is always the same number, then the sequnce is arithmetic sequence.
If the first term is called
Geometric:
“If the ratio of consecutive terms in a sequence is constant, then the sequnce is a geometric sequence.
If the first term is called
Calculation:
From the given sequence, the first, second, third and fourth term are
Obtain the difference between the consecutive terms.
Compute
Compute
Compute
Since the difference between the consecutive terms is not constant, the given sequence is not arithmetic.
Therefore, the sequence
Obtain the ratio of the consecutive terms.
Compute
Compute
Compute
Clearly, the common ratio is
Since the ratio of the consecutive terms is constant, the given sequence is geometric.
Therefore, the sequence
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Chapter 13 Solutions
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