Geometric and 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. This difference is called the common difference.

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

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n+1} - a_n.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_{n+1} / a_n.

Front

What is the explicit formula for an arithmetic sequence?

Back

Front

What is the explicit formula for a geometric sequence?

Back

Front

Identify if the sequence 52.5, 31.5, 18.9, 11.34 is arithmetic or geometric.

Back

The sequence is geometric.

Front

Identify if the sequence 52.5, 37.5, 22.5, 7.5 is arithmetic or geometric.

Back

The sequence is arithmetic.

Front

Identify if the sequence 13, 18, 23, 28 is arithmetic or geometric.

Back

The sequence is arithmetic.

Front

What is the common difference of the arithmetic sequence 5, 10, 15, 20?

Back

The common difference is 5.