Explicit and Recursive Rule

Front

What is an explicit rule in a sequence?

Back

An explicit rule defines the nth term of a sequence directly as a function of n, allowing you to calculate any term without needing to know the previous terms.

Tags

CCSS.HSF.BF.A.2

Front

What is a recursive rule in a sequence?

Back

A recursive rule defines each term of a sequence based on the previous term(s), requiring knowledge of earlier terms to find the next term.

Tags

CCSS.HSF.BF.A.2

Front

Given the sequence 7, 14, 28, 56, 112, what is the recursive formula?

Back

f(n) = f(n-1) * 2, f(1) = 7.

Tags

CCSS.HSF.IF.A.3

Front

What is the explicit formula for the sequence defined by a_n = 3(4)^n?

Back

The explicit formula is a_n = 3(4)^n, where n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the first four terms of the sequence a_n = 3(4)^n?

Back

Substitute n = 1, 2, 3, 4 into the formula: 12, 48, 192, 768.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the sequence defined by a_n = 7(n + 2)?

Back

The explicit formula is a_n = 7(n + 2), where n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the first four terms of the sequence a_n = 7(n + 2)?

Back

Substitute n = 1, 2, 3, 4 into the formula: 21, 28, 35, 42.

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

Given the arithmetic sequence -3, -8, -13, -18, what are the next three terms?

Back

The next three terms are -23, -28, -33.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in the arithmetic sequence -3, -8, -13, -18?

Back

The common difference is -5.

Tags

CCSS.HSF.BF.A.2