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

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

How do you find the common ratio of a geometric sequence?

Back

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

Front

What does a_1 represent in a geometric sequence?

Back

a_1 represents the first term of the geometric sequence.

Front

Write the general formula for the n-th term of a geometric sequence.

Back

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

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?

Back

The 4th term is a_4 = 3 * 2^(4-1) = 3 * 8 = 24.

Front

Is the sequence 2, 6, 18, 54,... geometric?

Back

Yes, the sequence is geometric with a common ratio of 3.

Front

What is the common ratio of the sequence 5, 15, 45, 135,...?

Back

The common ratio is 3.

Front

Given the sequence 81, 27, 9,..., write the rule a_n using the geometric sequence formula.

Back

a_n = 81 * (1/3)^(n-1).

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms?

Back

The terms of the sequence will decrease and approach zero.