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 a geometric sequence.

Front

Identify if the sequence is geometric: 2, 4, 8, 16...

Back

Yes, this is a geometric sequence with a common ratio of 2.

Front

Identify if the sequence is geometric: 5, 10, 15, 20...

Back

No, this is an arithmetic sequence.

Front

Write the explicit formula for the geometric sequence: 3, 6, 12, 24...

Back

a_n = 3(2)^(n-1)

Front

Find the common ratio for the sequence: 10, 30, 90, 270...

Back

The common ratio is 3.

Front

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

Back

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

Front

Determine the common ratio for the sequence: 1, 1/2, 1/4, 1/8...

Back

The common ratio is 1/2.

Front

Is the sequence 1, 2, 4, 8, 16... geometric?

Back

Yes, this is a geometric sequence with a common ratio of 2.

Front

Find the common ratio for the sequence: 5, -15, 45, -135...

Back

The common ratio is -3.