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 formula for 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 does the common ratio represent in a geometric sequence?

Back

The common ratio is the factor by which each term in the sequence is multiplied to get the next term.

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 (r = a_n / a_(n-1)).

Front

What is the first term of a geometric sequence denoted as?

Back

The first term of a geometric sequence is denoted as a_1.

Front

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

Back

The 4th term is 5 * 3^(4-1) = 5 * 27 = 135.

Front

What is a recursive formula for a geometric sequence?

Back

A recursive formula for a geometric sequence is a_n = r * a_(n-1), where r is the common ratio.

Front

What is the 3rd term of the geometric sequence 2, 6, 18, ...?

Back

The 3rd term is 18.

Front

What is the 5th term of the geometric sequence 4, 12, 36, ...?

Back

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

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms?

Back

The terms of the sequence decrease by half with each subsequent term.