Understanding Arithmetic Sequences and Linear Functions

This video tutorial explains how arithmetic sequences can be represented as linear functions. It covers function notation, graphing ordered pairs, and deriving explicit rules for sequences. The tutorial also addresses common misunderstandings about arithmetic sequences and demonstrates how to calculate specific terms using the explicit rule. By graphing these sequences, the video shows their linear nature and how they relate to linear functions.

What does function notation help us understand about a relation?

• It only applies to quadratic functions.

• It is used for non-linear equations.

• It relates the domain to the range.

• It shows the relation is not a function.

How do you find the value of f(x) when x is 4 in the function f(x) = 3x - 2?

• By adding 4 to the function.

• By dividing 4 by 3 and adding 2.

• By multiplying 4 by 2 and subtracting 3.

• By substituting 4 into the function and simplifying.

What is a common misunderstanding about arithmetic sequences?

• They must have a constant difference between terms.

• They always have a decreasing pattern.

• They can have a non-constant difference.

• They are the same as geometric sequences.

What is the explicit rule for an arithmetic sequence?

• 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)

How do you determine the eighth term of an arithmetic sequence using the explicit rule?

• By multiplying the first term by 8.

• By subtracting 8 from the common difference.

• By using the formula a_n = a_1 + d(n - 1) with n = 8.

• By adding 8 to the first term.

What does the x-axis represent when graphing an arithmetic sequence as a linear function?

• The sequence sum

• The term value

• The term number

• The common difference

How can an arithmetic sequence be represented on a coordinate plane?

• As a quadratic curve

• As a series of disconnected points

• As a circle

• As a line connecting ordered pairs