Understanding Arithmetic Sequences and Functions

The video tutorial explains how to solve arithmetic sequence word problems. It begins with an overview of arithmetic sequences, highlighting the importance of identifying key phrases that indicate addition or subtraction of a constant amount. The tutorial provides real-life examples, such as weight loss and earnings, to illustrate arithmetic sequences. It introduces the general formula T(n) = a + Dn, where 'a' is the initial term and 'D' is the common difference. The video then presents a detailed example involving Zachary's savings, demonstrating how to apply the formula to determine the number of weeks required to reach a savings goal of $750.

What is an arithmetic sequence?

• A sequence where each term is multiplied by a constant.

• A sequence where each term is added or subtracted by a constant.

• A sequence where each term is divided by a constant.

• A sequence where each term is a square of the previous term.

Which phrase indicates an arithmetic sequence in a word problem?

• The amount is squared each time.

• The amount increases by a fixed number each time.

• The amount is halved each time.

• The amount doubles every time.

If you earn $11.50 per hour, what type of sequence does this represent?

• Arithmetic sequence

• Fibonacci sequence

• Exponential sequence

• Geometric sequence

What is the general formula for an arithmetic sequence?

• T(n) = a * D^n

• T(n) = a + D * n

• T(n) = a / D + n

• T(n) = a - D * n

In the formula T(n) = a + D * n, what does 'a' represent?

• The first term

• The common difference

• The term number

• The last term

In the formula T(n) = a + D * n, what does 'D' represent?

• The common difference

• The first term

• The term number

• The last term

What is the common difference in Zachary's savings sequence?

• $28

• $68

• $20

• $40

What does the term 'n' represent in the formula T(n) = a + D * n?

• The term number

• The last term

• The first term

• The common difference

What is the initial amount Zachary has for his savings?

• $28

• $40

• $68

• $96

What is the significance of the number 40 in Zachary's savings equation?

• It is the weekly savings.

• It is the initial amount.

• It is the total savings goal.

• It is the common difference.