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 explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is given by 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

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term, r = a_n / a_(n-1).

Front

Given the sequence 3, -12, 48, -192, what is the common ratio?

Back

The common ratio is -4.

Front

What is the 9th term of the geometric sequence 4, 8, 16, 32?

Back

The 9th term is 1,024.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 54.

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

What are the next three terms in the sequence -4, -12, -36, -108?

Back

The next three terms are -324, -972, -2916.

Front

What is the common ratio for the sequence 28, 14, 7, 3.5?

Back

The common ratio is 1/2.

Front

Which sequence is represented by the equation 2(7)^(n-1)?

Back

The sequence is 2, 14, 98, 686...