Geometric Sequences

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 identify a geometric sequence?

Back

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

Front

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

Back

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

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

Given the sequence 2, 6, 18, 54, what is the common ratio?

Back

The common ratio is 3.

Front

Find the first four terms of the geometric sequence defined by a_n = 3(2)^(n-1).

Back

The first four terms are 3, 6, 12, 24.

Front

Is the sequence 5, 10, 20, 40 geometric or arithmetic?

Back

The sequence is geometric.

Front

What is the common ratio for the sequence 7, 21, 63?

Back

The common ratio is 3.

Front

If a geometric sequence has a first term of 4 and a common ratio of 1/2, what are the first four terms?

Back

The first four terms are 4, 2, 1, 0.5.

Front

How do you find the common ratio from the terms of a geometric sequence?

Back

To find the common ratio, divide any term by the previous term.