A tower is made of grey and white cubes. The first layer of the tower is made with one grey cube. A

Question

A tower is made of grey and white cubes. The first layer of the tower is made with one grey cube.

A tower with two layers is made with five grey cubes and one white cube as shown below.

A tower with three layers is made with nine grey cubes and six white cubes as shown below.

Complete the table below.
Number of layers
$1$
$2$
$3$
$4$
$5$
Total number of white cubes
$0$
$1$
$6$
Total number of grey cubes
$1$
$5$
$9$
Total number of cubes
$1$
$6$
$15$
Find, in terms of $n$, the total number of grey cubes in a tower with $n$ layers.
Find, in terms of $n$, the total number of cubes in a tower with $n$ layers.
Sarah used $\mathrm{97}$ grey cubes to build a tower. Calculate the number of white cubes she used.

Accepted Answer

(a) White: $0,1,6,15,28$; grey: $1,5,9,13,17$; total: $1,6,15,28,45$. (b) $4n-3$. (c) $2n^2-n$. (d) $1128$.

Number of layers	\(1\)	\(2\)	\(3\)
Total number of white cubes	\(0\)	\(1\)	\(6\)
Total number of grey cubes	\(1\)	\(5\)	\(9\)
Total number of cubes	\(1\)	\(6\)	\(15\)

IP1U7 HOT Q3