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

Given the sequence 2, 6, 18, 54, what is the common ratio?

Back

3

Front

How do you find the next term in a geometric sequence?

Back

Multiply the last term by the common ratio.

Front

If the first term a1 = 4 and the common ratio r = 2, what is the second term a2?

Back

8

Front

What is the formula for the nth 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 a geometric sequence has a first term of 5 and a common ratio of 3, what is the 4th term?

Back

135

Front

What does a1 represent in a geometric sequence?

Back

a1 represents the first term of the sequence.

Front

In the sequence defined by a_n = 3 * 4^(n-1), what is a5?

Back

768

Front

If the common ratio is 1/2, what happens to the terms of the sequence?

Back

The terms decrease and approach zero.