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 by the previous term in the sequence.

Front

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

Back

15 (3 * 5 = 15).

Front

What are the next three terms in the geometric sequence: 2, 6, 18, ___, ___, ___?

Back

54, 162, 486 (common ratio is 3).

Front

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

Back

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

Front

What is the common ratio for the sequence: 81, 27, 9, 3...?

Back

1/3 (27/81 = 1/3).

Front

If a geometric sequence has a common ratio of 2, what is the 4th term if the first term is 5?

Back

40 (5 * 2^3 = 40).

Front

What is the common ratio for the sequence: 64, 32, 16, 8...?

Back

1/2 (32/64 = 1/2).

Front

To find the next term in a geometric sequence, you should...

Back

multiply the last term by the common ratio.

Front

What is the common ratio for the sequence: 10, 20, 40, 80...?

Back

2 (20/10 = 2).