Arithmetic and Geometric Sequences Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

Front

How do you identify an arithmetic sequence?

Back

To identify an arithmetic sequence, check if the difference between consecutive terms is the same. If it is, the sequence is arithmetic.

Front

How do you identify a geometric sequence?

Back

To identify a geometric sequence, check if the ratio of consecutive terms is constant. If it is, the sequence is geometric.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the fixed amount multiplied to each term to get the next term in a geometric sequence.

Front

Is the sequence {5, 10, 15, 20, ...} arithmetic, geometric, or neither?

Back

Arithmetic (common difference of 5).

Front

Is the sequence {2, 4, 8, 16, ...} arithmetic, geometric, or neither?

Back

Geometric (common ratio of 2).

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.