Algebra II : Summations and Sequences
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #15 : Other Sequences And Series
Evaluate:
Example Question #16 : Other Sequences And Series
A sequence begins as follows:
Which statement is true?
The sequence cannot be arithmetic or geometric.
The sequence may be geometric.
None of these
The sequence may be arithmetic.
All of these
The sequence cannot be arithmetic or geometric.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the difference between each term and the previous term varies from term to term:
The first difference:
The second difference:
The sequence cannot be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one varies from term to term:
The first ratio:
The second ratio:
The sequence cannot be geometric.
Example Question #17 : Other Sequences And Series
A sequence begins as follows:
Which statement is true?
The sequence may be arithmetic.
The sequence cannot be arithmetic or geometric.
All of these
The sequence may be geometric.
None of these
The sequence cannot be arithmetic or geometric.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the difference between each term and the previous term varies from term to term:
The sequence cannot be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one varies from term to term:
The sequence cannot be geometric.
Example Question #18 : Other Sequences And Series
A sequence begins as follows:
Which statement is true?
The sequence may be geometric.
The sequence may be arithmetic.
None of these
The sequence cannot be arithmetic or geometric.
All of these
The sequence cannot be arithmetic or geometric.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the difference between each term and the previous term varies from term to term:
The sequence cannot be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratio of each term to the previous one also varies from term to term:
The sequence cannot be geometric.
Example Question #21 : Other Sequences And Series
A sequence begins as follows:
Which statement is true?
The sequence cannot be arithmetic or geometric.
The sequence may be arithmetic and geometric.
None of these
The sequence may be arithmetic.
The sequence may be geometric.
The sequence cannot be arithmetic or geometric.
An arithmetic sequence is one in which each term is generated by adding the same number - the common difference - to the previous term. As can be seen here, the differences between each term and the previous term is not constant from term to term:
The sequence cannot be arithmetic.
A geometric sequence is one in which each term is generated by multiplying the previous term by the same number - the common ratio. As can be seen here, the ratios of each term to the previous one is not constant from term to term:
The sequence cannot be geometric.
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