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 does 'r' represent in a geometric sequence?

Back

In a geometric sequence, 'r' represents the common ratio, which is the factor by which we multiply each term to get the next term.

Front

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

Back

324, 972, 2916

Front

If a₃ = 224 and r = -½, what is the eighth term of the geometric sequence?

Back

-7

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 = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.

Front

Find the first four terms of the sequence given the rule: a_n = 4(5)^n-1

Back

4, 20, 100, 500

Front

What is the common ratio if the first term is 3 and the second term is 12?

Back

The common ratio is 4, since 12 / 3 = 4.

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 fifth term of the geometric sequence: 2, 6, 18, 54, ...?

Back

The fifth term is 162.

Front

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the fourth term?

Back

The fourth term is 40.