Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.
figure 1: 9 cubes
figure 2: 13 cubes
figure 3: (blank)
figure 4: (blank)
figure 5: (blank)
Let
f(0)=5
so
For n=0
f(1)=5+4=9
f(1)=9
For n=1
f(2)=9+4=13
f(2)=13
For n=2
f(3)=13+4=17
For n=3
f(4)=17+4=21
For n=4
f(5)=21+4=25
For n=5
f(6)=25+4=29
therefore
theanswer is
figure 3: 17
figure 4: 21
figure 5: 25