Geometric/Arithmetic Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that is 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 constant factor by which each term is multiplied to get the next term in a geometric sequence.

Front

Identify the common difference in the sequence: 4, 7, 10, 13,...

Back

The common difference is 3.

Front

Identify the common ratio in the sequence: 2, 6, 18, 54,...

Back

The common ratio is 3.

Front

What is the explicit formula for the arithmetic sequence: 5, 10, 15,...?

Back

a_n = 5 + 5(n-1) or a_n = 5n.

Front

What is the explicit formula for the geometric sequence: 3, 9, 27,...?

Back

a_n = 3 * 3^(n-1).

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.