Question

Sonal and Amole made a sequence of tile designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.
Draw a graph using the first five pairs of numbers in your table.

Answer 1

From the given diagrams, we can conclude that the given data forms Arithmetic Progression series. The graph is plotted as above.

When side of purple tile is $1$, number of white tiles on border is $8$

When side of purple tile is $2$, number of white tiles on border is $12$

When side of purple tile is $3$, number of white tiles on border is $16$

Thus, using formula of AP to find further values of number of white tiles on border.

$a_n=a_1+(n-1)d$

1) When $n=4$,

$a_3=8+(4-1)\times 4$

$\therefore a_3=8+12=20$

2) When $n=5$,

$a_4=8+(5-1)\times 4$

$\therefore a_4=8+16=24$