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 determine if a sequence is geometric?

Back

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

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 geometric sequence 3, 6, 12, ..., what is the common ratio?

Back

The common ratio is 2.

Front

Find the next three terms in the geometric sequence: 2, 6, 18, ...

Back

The next three terms are 54, 162, 486.

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the second term?

Back

The second term is 15.

Front

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

Back

The nth term 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

Determine whether the sequence 4, 12, 36, ... is arithmetic, geometric, or neither.

Back

The sequence is geometric.

Front

Find the common ratio for the geometric sequence: 81, 27, 9, ...

Back

The common ratio is 1/3.

Front

What are the next three terms in the geometric sequence: 1000, 500, 250, ...?

Back

The next three terms are 125, 62.5, 31.25.