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

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

Back

6

Front

Calculate the 4th term of the geometric sequence defined by a_n = 3 * 2^(n-1).

Back

12

Front

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

Back

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

Front

Find the next term in the geometric sequence: 5, 15, 45, ...

Back

135

Front

What is the 5th term of the sequence defined by a_n = 4 * (1/2)^(n-1)?

Back

1

Front

If a geometric sequence has a first term of 10 and a common ratio of 1/2, what is the 6th term?

Back

0.15625

Front

What are the next three terms in the geometric sequence: 81, 27, 9, ...?

Back

3, 1, 1/3

Front

In the sequence 64, 32, 16, what is the common ratio?

Back

1/2