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

The nth term of a geometric sequence 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

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

Back

4, 20, 100, 500

Front

Is the sequence -4, -12, -36, -108,... geometric?

Back

Yes, it is geometric with a common ratio of 3.

Front

Is the sequence 9, 99, 999, 9999,... geometric?

Back

No, it is not geometric.

Front

Write an explicit rule for the general term of the sequence 5, 15, 45,...

Back

a_n = 5(3)^(n-1)

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54?

Back

The common ratio is 3.

Front

How do you determine if a sequence is geometric?

Back

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

Front

What is the common ratio of the sequence 10, 30, 90, 270?

Back

The common ratio is 3.

Front

If the first term of a geometric sequence is 7 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 7 * 2^(5-1) = 112.