Arithmetic Sequences and Linear Functions

The video tutorial explains arithmetic sequences and their representation as linear functions. It covers function notation, common misunderstandings, and the explicit rule for arithmetic sequences. The tutorial demonstrates how to graph these sequences and verify their linearity by plotting points on a coordinate plane.

What does the graph of the sequence a_n = 1 + 3(n - 1) represent?

• An exponential function

• A logarithmic function

• A linear function

• A quadratic function

In function notation, what does f(x) represent?

• The domain of the function

• The intercept of the function

• The range of the function

• The slope of the function

What is the value of f(x) when x = 4 for the function f(x) = 3x - 2?

• 12

• 10

• 14

• 8

What is a common misunderstanding about arithmetic sequences?

• They always have a constant difference

• They can have varying differences

• They are always decreasing

• They are always increasing

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)

If the first term of an arithmetic sequence is 1 and the common difference is 3, what is the 8th term?

• 20

• 21

• 22

• 23

How is the term number represented on a coordinate plane for an arithmetic sequence?

• As the y-axis

• As the slope

• As the intercept

• As the x-axis

What does the explicit rule a_n = 3n - 2 represent when graphed?

• A circle

• A parabola

• A line

• A hyperbola

What ordered pair represents the 8th term of the sequence on a graph?

• (8, 23)

• (8, 20)

• (8, 22)

• (8, 21)

What is the relationship between the explicit rule of an arithmetic sequence and a linear function?

• They both represent a quadratic function

• They both represent a constant rate of change

• They both represent exponential growth

• They are unrelated