Question

Describe how the pattern is changing in words: adding one tile each time.

a) The pattern is increasing by one tile with each step.
b) The pattern is decreasing by one tile with each step.
c) The pattern is alternating between adding and subtracting tiles.
d) The pattern is randomly changing.

Write an algebraic rule for this pattern: Y=n+6.
a) Y=n+6
b) Y=n−6
c) Y=n×6
d) Y=n ^2+6

Answer 1

For the given question, the correct choices are:

a) The pattern is increasing by one tile with each step.

a) Y=n+6

Step-by-step explanation:

Part 1: Pattern Change Description

In the first part of the question, option (a) "The pattern is increasing by one tile with each step" accurately describes the change in the pattern. This means that for each step or iteration, one tile is added to the existing pattern. This is a straightforward and clear description of the pattern's evolution.

Part 2: Algebraic Rule and Explanation

Moving on to the algebraic rule Y=n+6, we can break it down to understand its components. The variable Y represents the total number of tiles, and 'n' represents the step or iteration number. The expression 'n+6' signifies that for each step, the value of 'n' is added to a constant value of 6, resulting in the total number of tiles.

To illustrate, if we substitute 'n' with 1 (for the first step), the equation becomes Y=1+6, yielding 7 tiles. Similarly, for the second step, Y=2+6, resulting in 8 tiles, and so on. This demonstrates a consistent increase of one tile with each step, aligning with the given pattern.

In summary, option (a) accurately describes the pattern change, and option (a) Y=n+6 provides the correct algebraic rule, showcasing a linear progression where the total number of tiles increases by one with each step.