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 formula for the nth term of a geometric sequence?

Back

Front

Find the first four terms of the sequence given the rule: a_n = 4(5)^(n-1)

Back

The first four terms are: 4, 20, 100, 500.

Front

Write the explicit rule for the geometric sequence: 2, -12, 72, ...

Back

Front

Find the 9th term in the geometric sequence: 4, 8, 16, 32, ...

Back

The 9th term is: 1,024.

Front

Write the explicit formula for the geometric sequence: 3, 24, 192, 1536

Back

Front

Is the sequence 2, 4, 12, 48 geometric?

Back

No, the sequence is not geometric because the ratio between consecutive terms is not constant.

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

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

Front

How do you determine if a sequence is geometric?

Back

To determine if a sequence is geometric, check if the ratio of consecutive terms is constant.