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 nth term of a geometric sequence?

Back

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

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 a_3 = 224 and r = -1/2, how do you find a_1?

Back

Use the formula a_n = a_1 * r^(n-1). For a_3, we have 224 = a_1 * (-1/2)^(3-1). Solve for a_1.

Front

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

Back

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

Front

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

Back

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

Front

Given a_1 = 10 and a_n = a_(n-1) * 3, what are the first four terms?

Back

The first four terms are: 10, 30, 90, 270.

Front

Identify the common ratio in the sequence a_n = 7(1/2)^(n-1).

Back

The common ratio is 1/2.

Front

How do you find the next terms in a geometric sequence?

Back

Multiply the last known term by the common ratio to find the next term.

Front

Find the next three terms for the geometric sequence: 2, -12, 72, ...

Back

The next three terms are: -432, 2592, -15552.