Arithmetic Sequences and Explicit Rules

The video tutorial explains the relationship between arithmetic explicit and recursive rules. It describes the form of arithmetic explicit rules, which include the first term and the common difference, and how these relate to the recursive rule. The tutorial provides an example to illustrate how to derive an explicit rule from a given recursive rule, emphasizing the importance of understanding the components such as the first term and the common difference.

What is the general form of an arithmetic explicit rule?

• a(n) = a(1) * d(n-1)

• a(n) = a(1) + d(n-1)

• a(n) = a(1) - d(n-1)

• a(n) = a(1) / d(n-1)

In the context of arithmetic explicit rules, what does 'a(1)' represent?

• The first term or starting value

• The last term

• The common difference

• The term number

What is the role of 'd' in the arithmetic explicit rule formula?

• It is the first term

• It is the common difference between terms

• It is the last term

• It is the term number

How do you determine the common difference in an arithmetic sequence?

• By dividing the first term by the last term

• By finding the difference between consecutive terms

• By adding the first term to the last term

• By subtracting the first term from the last term

If the first term of a sequence is 4 and the common difference is 2, what is the explicit rule?

• a(n) = 4 + 2(n-1)

• a(n) = 4 - 2(n-1)

• a(n) = 4 * 2(n-1)

• a(n) = 4 / 2(n-1)

What operation is performed with the common difference in the explicit rule formula?

• Addition

• Subtraction

• Division

• Multiplication