a Start by determining the total number of small triangles in each figure.
B
b Use the function you wrote in Part A.
A
a f(n)=4^(n-1)
B
b The 10th figure will be a large triangle containing 262 144 small triangles.
Practice makes perfect
a We see that the first figure is just a triangle. The second figure is a triangle divided into 4 small triangles, and the third triangle is divided into 16 small triangles.
The number of small triangles for each figure is 4 times that of the previous figure. Hence, there is a common ratio of 4. The number of triangles is 1 for the first figure. We can write the function since a_1= 1 and r= 4.
f(n)= a_1( r)^(n-1) ⇔ f(n)= 1( 4)^(n-1)
The function f(n)=4^(n-1) gives the number of small triangles in the large triangle for the nth figure.
b Using the function in Part A, we can find the number of small triangles for the 10th figure.
