Linear Functions and Arithmetic Sequences

This video tutorial covers linear functions and arithmetic sequences, focusing on writing explicit formulas for arithmetic sequences. It compares linear functions, which have a continuous relationship, to arithmetic sequences, which are discrete. The video explains how to write equations for both using point-slope form and provides examples of finding explicit formulas for arithmetic sequences with given terms. It also demonstrates how to handle sequences with non-consecutive terms by treating them as points on a line.

What is the main focus of the video on linear functions and arithmetic sequences?

• How to graph linear functions

• How to find the area of a circle

• How to rate explicit formulas for arithmetic sequences

• How to solve quadratic equations

What is the key difference between a linear function and an arithmetic sequence?

• Linear functions are discrete, arithmetic sequences are continuous

• Linear functions are continuous, arithmetic sequences are discrete

• Linear functions have a variable rate of change, arithmetic sequences have a constant rate

• Linear functions are always increasing, arithmetic sequences are always decreasing

What is the term used to describe the constant rate of change in a linear function?

• Axis

• Vertex

• Slope

• Intercept

In an arithmetic sequence, what is the term for the constant amount added or subtracted each time?

• Slope

• Intercept

• Variable

• Common difference

What form is emphasized for writing equations in the video?

• Quadratic form

• Point-slope form

• Slope-intercept form

• Standard form

Which notation is typically used for linear functions?

• Function notation

• Vector notation

• Matrix notation

• Subscript notation

What is the equivalent of the slope in an arithmetic sequence?

• Intercept

• Variable

• Common difference

• Coefficient

In point-slope form, what do x1 and y1 represent?

• The maximum and minimum values of a function

• The first and second terms of a sequence

• The x and y coordinates of a point on the line

• The slope and intercept

What is the common difference in the sequence 14, 11, 8, 5?

• -3

• 4

• -4

• 3

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

• By adding the first and last terms

• By subtracting consecutive terms

• By dividing the first term by the last term

• By multiplying the first term by the last term