Answer:
figure 3: 17 cubes.
figure 4: 21 cubes.
figure 5: 25 cubes.
Step-by-step explanation:
Let the nth figure be represented by f(n).
also we are given f(n+1)=f(n)+4.
The number of cubes used in figure 1 i.e. f(1) is 9.
number of cubes used in figure 2 i.e. f(2) is 13
Now we have to find the number of cube used in figure 3, figure 4 and figure 5.
number of cubes in figure 3 i.e. f(3)=f(2)+4=13+4=17.
number of cubes in figure 4 i.e. f(4)=f(3)+4=17+4=21.
number of cubes in figure 5 i.e. f(5)=f(4)+4=21+4=25.
Answer:
Figure 3: 17 cubes
Figure 4: 21 cubes
Figure 5: 25 cubes
Step-by-step explanation:
Luis uses cubes to represent each term of a pattern based on a recursive function.
The given recursive function defined as
[tex]f(n+1)=f(n)+4[/tex] .... (1)
where n is an integer and n ≥ 2.
It is given
Figure 1: 9 cubes
Figure 2: 13 cubes
[tex]f(1)=9, f(2)=13[/tex]
Substitute n=2 in equation (1).
[tex]f(2+1)=f(2)+4[/tex]
[tex]f(3)=13+4[/tex]
[tex]f(3)=17[/tex]
Substitute n=3 in equation (1).
[tex]f(3+1)=f(3)+4[/tex]
[tex]f(4)=17+4[/tex]
[tex]f(4)=21[/tex]
Substitute n=4 in equation (1).
[tex]f(4+1)=f(4)+4[/tex]
[tex]f(5)=21+4[/tex]
[tex]f(5)=25[/tex]
Therefore, the number of cubes in figure 3, 4 and 5 are 17, 21 and 25 respectively.
