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 (r) is the factor by which we multiply each term to get the next term in the sequence.

Front

Find the common ratio: 4, -16, 64, -256, ...

Back

r = -4

Front

Find the common ratio for the geometric sequence: 10, 1/2, 2, 4

Back

r = 2

Front

Which of the following is a geometric sequence? 1, 4, 7, 10, ...; 1, 2, 6, 24, ...; 1, 1, 2, 3, ...; 1, 3, 9, 27, ...

Back

1, 3, 9, 27, ...

Front

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

Back

a_n = 3(-4)^(n-1)

Front

What are the next 3 terms in the following geometric sequence: 512, 256, 128, ___, ___, ___, ...

Back

64, 32, 16

Front

How do you find 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

What is the first term of the geometric sequence: 5, 15, 45, ...?

Back

The first term (a_1) is 5.

Front

If the common ratio is 3, what is the second term if the first term is 4?

Back

The second term is 4 * 3 = 12.