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 a geometric sequence where a_1 = 10 and a_n = a_(n-1) * 3, what are the first four terms?

Back

10, 30, 90, 270.

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_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Find a_12 for the rule a_n = 6(2)^(n-1).

Back

12,288.

Front

What are the next three terms in the geometric sequence: 64, 16, 4...?

Back

1, ¼, 1/16.

Front

How do you write the recursive rule for a geometric sequence?

Back

The recursive rule is written as a_1 = first term; a_n = a_(n-1) * r, where r is the common ratio.

Front

What is the common ratio for the geometric sequence: 64, 16, 4...?

Back

¼.

Front

If a geometric sequence has a_1 = 64 and a common ratio of ¼, what is a_3?

Back

a_3 = 64 * (¼)^(3-1) = 4.

Front

What is the relationship between the terms in a geometric sequence?

Back

Each term is obtained by multiplying the previous term by the common ratio.