U7D10 Flashcardziz: 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

How do you find the common ratio in a geometric sequence?

Back

To find the common ratio, divide any term in the sequence by the previous term (r = a_n / a_(n-1)).

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what are the first four terms?

Back

3, 6, 12, 24

Front

What does a_n represent in a geometric sequence?

Back

a_n represents the nth term of the geometric sequence.

Front

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

Back

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

Front

If a geometric sequence has a common ratio of -3, what is the second term if the first term is 4?

Back

The second term is -12 (4 * -3).

Front

What are the next three terms in the geometric sequence: 81, 27, 9, ___, ___, ___?

Back

3, 1, 1/3

Front

In the sequence 5, 15, 45, what is the common ratio?

Back

The common ratio is 3 (15/5 = 3 and 45/15 = 3).

Front

What does a_(n-1) represent in a geometric sequence?

Back

a_(n-1) represents the term before the nth term.

Front

If the first term of a geometric sequence is 2 and the common ratio is 1/2, what are the first four terms?

Back

2, 1, 1/2, 1/4