Sequences - Recursive Formulas

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Tags

CCSS.HSF.BF.A.2

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

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

How do you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, calculate the difference between consecutive terms. If the difference is constant, it is arithmetic.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is geometric?

Back

To determine if a sequence is geometric, calculate the ratio of consecutive terms. If the ratio is constant, it is geometric.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) of a geometric sequence 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.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

Identify the common difference for the arithmetic sequence: 5, 10, 15, 20, ...

Back

The common difference is 5.

Tags

CCSS.HSF.BF.A.2