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 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 a geometric sequence.

Front

Identify the common ratio in the sequence: 3, 6, 12, 24.

Back

The common ratio is 2.

Front

Is the sequence {5, 10, 20, 40} arithmetic, geometric, or neither?

Back

Geometric.

Front

What are the next three terms in the geometric sequence: 4, 12, 36, ___, ___, ___?

Back

108, 324, 972.

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 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

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 5th term?

Back

The 5th term is 162.

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum S_n of the first n terms is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

Is the sequence {1, 1/2, 1/4, 1/8} arithmetic, geometric, or neither?

Back

Geometric.