a Start by determining the total number of small squares in each figure.
B
b Use the function you write in Part A.
A
a f(n)=9^(n-1)
B
b The 10th figure will be a large square containing 387 420 489 small squares.
Practice makes perfect
a We see that the first figure is just a square and the second figure is a square divided into 9 small squares. The third square is divided into 81 small squares.
There is a common ratio of 9 between the number of small squares contained in a large square. The number of squares contained in the first figure is 1. We can write the function since a_1= 1 and r= 9.
f(n)= a_1( r)^(n-1) ⇔ f(n)= 1( 9)^(n-1)
The function f(n)=9^(n-1) represents the number of small squares contained in the large square of the nth figure.
b Using the function in Part A, we can find the number of small squares for the 10th figure.
