Generate two numerical patterns using two given rules

What you'll learn

1. Generate two numerical sequences from two given rules and the same starting number, recording at least five terms of each sequence in a two-column table.
2. Identify the apparent relationship between corresponding terms in the two sequences (e.g., "each term in Sequence B is always twice the corresponding term in Sequence A").
3. Form ordered pairs by pairing corresponding terms from the two sequences, with the first sequence providing the x-coordinate and the second providing the y-coordinate.
4. Plot the ordered pairs on a first-quadrant coordinate plane and describe the visual pattern the points create.
5. Explain why a multiplicative rule relationship (such as "always double") produces points that fall along a straight line through the origin.
6. Predict later corresponding terms using the discovered relationship, without extending both sequences term by term.

Prerequisites

• Use a pair of perpendicular number lines, called axes, to define a coordinate system