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 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 geometric sequence 3, 9, 27, what is the common ratio?

Back

The common ratio is 3, since 9/3 = 3 and 27/9 = 3.

Front

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

Back

The nth term (a_n) 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

The next term is 135.

Front

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

Back

The 4th term is 128.

Front

What is the next term of the geometric sequence: 2, 10, 50...?

Back

The next term is 250.

Front

What is the next term of the geometric sequence: 250, 50, 10...?

Back

The next term is 2.

Front

Find the next three terms of the sequence: 4, 12, 36, 108...

Back

The next three terms are 324, 972, 2916.

Front

What is the common ratio for the geometric sequence: 8, 4, 2...?

Back

The common ratio is 1/2.