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, r is the common ratio, and n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

4, 20, 100, 500

Tags

CCSS.HSF.BF.A.2

Front

If Daisy received $2 on her first birthday and the amount tripled each year, how much will she receive on her 5th birthday?

Back

$162

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in the sequence.

Tags

CCSS.HSF.BF.A.2

Front

What does 'r' represent in a geometric sequence?

Back

Common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the 9th term in a geometric sequence with a common ratio of 2 and a first term of 3?

Back

768

Tags

CCSS.HSF.BF.A.2

Front

How do you find the common ratio of a geometric sequence?

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Tags

CCSS.HSF.BF.A.2

Front

What is the relationship between the first term and the common ratio in a geometric sequence?

Back

The first term is multiplied by the common ratio raised to the power of (n-1) to find the nth term.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 10 and the common ratio is 3, what are the first three terms?

Back

10, 30, 90.

Tags

CCSS.HSF.BF.A.2