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 sequence 4, -16, 64, -256, what is the common ratio?

Back

r = -4.

Front

What are the next three terms in the geometric sequence 512, 256, 128, ...?

Back

64, 32, 16.

Front

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

Back

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

Front

Calculate a_5 in the sequence defined by a_n = 5 ⋅ 2^(n-1).

Back

a_5 = 80.

Front

What is the 5th term of the geometric sequence 4, 16, 64, ...?

Back

The 5th term is 256.

Front

If the first term of a geometric sequence is 10 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 270.

Front

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

Back

r = 3.

Front

If a geometric sequence has a common ratio of -2 and the first term is 5, what is the 3rd term?

Back

The 3rd term is 20.