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 geometric sequence 64, 16, 4, what is the common ratio?

Back

The common ratio is ¼.

Front

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

Back

The next three terms are 1, ¼, 1/16.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Write the explicit formula for the geometric sequence 3, -12, 48, -192.

Back

The explicit formula is a_n = 3(-4)^(n-1).

Front

What is the first term of the geometric sequence defined by a_n = 7(½)^(n-1)?

Back

The first term is 7.

Front

If the common ratio of a geometric sequence is negative, what does this imply about the terms?

Back

If the common ratio is negative, the terms of the sequence will alternate in sign.

Front

How can you determine if a sequence is geometric?

Back

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

Front

What is the common ratio of the sequence 2, -10, 50, -250?

Back

The common ratio is r = -5.