Algebra II : Other Sequences and Series

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2801 : Algebra Ii

A sequence begins as follows:

Which statement is true?

Possible Answers:

The sequence may be geometric.

The sequence cannot be arithmetic or geometric.

None of these

The sequence may be arithmetic.

The sequence may be arithmetic and geometric.

Correct answer:

The sequence cannot be arithmetic or geometric.

Explanation:

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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