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 find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last term by the common ratio.

Front

Given the sequence 4, 12, 36, 108, what are the next three terms?

Back

324, 972, 2916

Front

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

Back

The nth term of a geometric sequence can be expressed as a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

Find the first four terms of the sequence given the rule: a_n = 4(5)^(n-1).

Back

4, 20, 100, 500

Front

What are the next three terms in the geometric sequence: 512, 256, 128, ___, ___, ___?

Back

64, 32, 16

Front

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

Back

The common ratio can be found by dividing any term by the previous term.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what are the first four terms?

Back

3, 6, 12, 24

Front

What is the common ratio for the geometric sequence 10, 30, 90, ...?

Back

The common ratio is 3.

Front

If a geometric sequence has a common ratio of 1/2, what is the next term after 8?

Back

4.