Question

In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.

Write a function that models the total number of blocks in terms of n.

Answer 1

Figure 1
n=1→f(n)=f(1)=1

Options 2 or 3

Figure 2
n=2→f(n)=f(2)=5

With Option 2:
f(n)=f(n-1)+2n
n=2→f(2)=f(2-1)+2(2)
f(2)=f(1)+4=1+4→f(2)=5 ok

With Option 3
f(n)=f(n-1)+n
n=2→f(2)=f(2-1)+2
f(2)=f(1)+2=1+2→f(2)=3 No

Answer: Second option: f(1)=1; f(n)=f(n-1)+2n; for n>=2