Question

Carson uses cubes to make a pattern of shapes. The first shape has a height of

2 cubes and a length of 2 cubes, as shown below. For each step in the pattern,
Carson adds 1 cube to the height and I cube to the length. Which sentence
about the shapes in Carson's pattern is true?
Step 1
height
length
» The total number of cubes in each
shape will alternate between even and
odd.
» The length of each shape will alterrte
between even numbers and odd
numbers.
The total number of cubes in each
shape will be even.
The length of each shape will be an
even number.​

Answer 1

The total number of cubes in each shape will alternate between even and odd.

The length of each shape will alternate between even numbers and odd numbers

Explanation:

I have drawn a picture of the cubes below.

The cubes for Step 1 are black.

Those added in Step 2 are pink.

Each step has cubes of a different colour.

`\begin{array}{cccc}\textbf{Step} & \textbf{Height} &\textbf{Length} & \textbf{Cubes}\\1& 2 & 2 & 2\\2 & 3 & 3 & 9\\3& 4 & 4 & 16\\4 & 5 & 5 & 25\\5 & 6 & 6 & 36\\\end{array}`

The total number of cubes in each shape (Column 4 in the table) alternates between even and odd.

The length of each shape (Column 3 in the table) alternates between even and odd.