Algebra II : Geometric Sequences

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #21 : Mathematical Relationships And Basic Graphs

A geometric sequence begins as follows:

Which of the following gives the definition of its th term?

Possible Answers:

Correct answer:

Explanation:

The th term of a geometric sequence is 

where  is its initial term and  is the common ratio between the terms. 

Substituting, the expression becomes 

By factoring and remultiplying, this becomes

Example Question #21 : Geometric Sequences

A sequence begins as follows:

Which statement is true?

Possible Answers:

The sequence may be geometric.

The sequence may be arithmetic.

None of these

The sequence cannot be arithmetic or geometric.

The sequence may be arithmetic and geometric.

Correct answer:

The sequence may be 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 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 is the same:

The sequence could be geometric.

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