### All Algebra II Resources

## Example Questions

### 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:**

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.

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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