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 common ratio in a geometric sequence?

Back

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

Front

Given the sequence 64, -16, 4, -1, what is the common ratio?

Back

r = -1/4.

Front

Given the sequence 4, -16, 64, -256, what is the common ratio?

Back

r = -4.

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

What is the recursive formula for a geometric sequence?

Back

The recursive formula is a_n = a_(n-1) * r.

Front

Find the next three terms in the sequence 4, 12, 36, 108.

Back

The next three terms are 324, 972, 2916.

Front

Write an explicit rule for the general term of the sequence 5, 15, 45.

Back

a_n = 5(3)^(n-1).

Front

What is the first term of the geometric sequence 3, 6, 12, 24?

Back

The first term (a_1) is 3.

Front

If the common ratio of a geometric sequence is 2, what are the first four terms starting from 1?

Back

The terms are 1, 2, 4, 8.