Geometric Sequence

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

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

Back

To find the next term, multiply the last known term by the common ratio.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula is given by a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

Given the sequence 512, 256, 128, what are the next three terms?

Back

64, 32, 16.

Front

Is the sequence -432, 72, -12, 2 geometric?

Back

Yes, it is geometric because each term is obtained by multiplying the previous term by a common ratio.

Front

What is the common ratio of the sequence 10, 40, 160, 640?

Back

The common ratio is 4.

Front

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

Back

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

Front

If a_n = 10(2)^(n-1), what is the common ratio?

Back

The common ratio is 2.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.