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

To find the common ratio, divide any term in the sequence by the previous term (r = a_n / a_(n-1)).

Front

What is the common ratio of the sequence 2, 6, 18, 54, ...?

Back

The common ratio is 3.

Front

Is the sequence 5, 10, 15, 20 arithmetic, geometric, or neither?

Back

The sequence is arithmetic.

Front

Is the sequence 3, 9, 27, 81 arithmetic, geometric, or neither?

Back

The sequence is geometric.

Front

What is the common ratio for the geometric sequence 4, -16, 64, -256, ...?

Back

The common ratio is -4.

Front

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the third term?

Back

The third term is 20.

Front

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

Back

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

Front

Find the common ratio for the geometric sequence 1, -1, 1, -1, ...

Back

The common ratio is -1.

Front

If a geometric sequence has a common ratio of 1/2 and the first term is 8, what is the fourth term?

Back

The fourth term is 1.