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.

Tags

CCSS.HSF.BF.A.2

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 = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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).

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The first four terms are 3, 6, 12, 24.

Tags

CCSS.HSF.BF.A.2

Front

What does a_1 represent in a geometric sequence?

Back

a_1 represents the first term of the geometric sequence.

Tags

CCSS.HSF.BF.A.2

Front

Find the common ratio for the sequence: 2, 6, 18, 54, ...

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio for the sequence: 5, 10, 20, 40, ...

Back

The common ratio is 2.

Tags

CCSS.HSF.BF.A.2

Front

If a geometric sequence has a common ratio of -3, what is the second term if the first term is 4?

Back

The second term is -12.

Tags

CCSS.HSF.BF.A.2

Front

What is the 5th term of the geometric sequence defined by a_n = 2(3)^(n-1)?

Back

The 5th term is 162.

Tags

CCSS.HSF.BF.A.2

Front

What does the term 'common ratio' mean?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Tags

CCSS.HSF.BF.A.2