Page 2: Further Examples and Equations

This page continues with another example of an arithmetic sequence and introduces equations for finding terms.

Example #2 is presented:

Example: Starting input: 0, Starting output: 1, Pattern: Adds 3 each time (common difference)

A table similar to the first example is provided, showing the relationship between x and f$x$ values.

The page then introduces equations for finding terms in arithmetic sequences:

1. When the starting input is 1: Output$x$ = Starting output ± Common difference $x-1$

2. When the starting input is 0: Output$x$ = Starting output ± Common difference $x$

Highlight: The choice of equation depends on whether the starting input is 0 or 1.

Examples of applying these equations are given:

For Example #1: f$x$ = 2 + 2$x-1$ For Example #2: f$x$ = 1 + 3x

Vocabulary: Term - A number in a sequence.

This page reinforces the concept that arithmetic sequences can be represented as linear functions, with the slope representing the common difference and the y-intercept representing the starting output.

Page 1: Introduction to Arithmetic Sequences

This page introduces the concept of arithmetic sequences and provides a detailed example.

An arithmetic sequence is defined as a sequence where the difference between consecutive terms is constant. The page explains that all sequences have a starting input (independent variable) and a starting output (dependent variable).

Definition: An arithmetic sequence is a sequence where each term differs from the previous term by a constant amount, called the common difference.

The page presents Example #1 of an arithmetic sequence:

Example: Starting input: 1, Starting output: 2, Pattern: Adds 2 each time (common difference)

A table is provided showing the relationship between input $x$ and output (f$x$) values:

x | f$x$ 1 | 2 2 | 4 3 | 6 4 | 8

Highlight: Arithmetic sequences are linear functions because they have a constant rate of change.

The page also includes a visual representation of the sequence, showing how each point rises by 2 and moves right by 1 on a coordinate plane.

Vocabulary: Common difference - The constant value added to each term to get the next term in an arithmetic sequence.