Geometric Sequences Practice

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 ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term in the sequence by the previous term: r = a_n / a_(n-1).

Front

Given the geometric sequence 64, 16, 4, what are the next three terms?

Back

1, ¼, 1/16.

Front

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

Back

The nth term can be expressed as a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Identify the common ratio in the sequence defined by a_n = 7(½)^(n-1).

Back

The common ratio is ½.

Front

What type of sequence is 400, 200, 100, 50, 25?

Back

It is a geometric sequence.

Front

What is the difference between arithmetic and geometric sequences?

Back

In an arithmetic sequence, each term is obtained by adding a constant (common difference), while in a geometric sequence, each term is obtained by multiplying by a constant (common ratio).

Front

If a sequence has a common difference of 5, what type of sequence is it?

Back

It is an arithmetic sequence.

Front

What is the first term of the sequence defined by a_1 = 10 and a_n = a_(n-1)(3)?

Back

The first term is 10.

Front

How do you determine if a sequence is geometric?

Back

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