A1 3.1 Geometric Sequences, explicit formula

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

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

Front

Given the geometric sequence 3, 6, 12, what is the common ratio?

Back

The common ratio is 2, since each term is multiplied by 2 to get the next term.

Front

Find the next three terms of the geometric sequence: 5, 15, 45, ...

Back

The next three terms are 135, 405, 1215.

Front

What is the difference between arithmetic and geometric sequences?

Back

In an arithmetic sequence, each term is obtained by adding a constant (common difference), while in a geometric sequence, each term is obtained by multiplying by a constant (common ratio).

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 to find the nth term of a geometric sequence?

Back

The nth term can be found using the formula a_n = a_1 * r^(n-1).

Front

If the first term of a geometric sequence is 4 and the common ratio is 3, what is the 5th term?

Back

The 5th term is 4 * 3^(5-1) = 4 * 81 = 324.

Front

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

Back

The common ratio is 3, since each term is multiplied by 3 to get the next term.