Question

Luis 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 Luis use in the third, fourth, and fifth figures of the pattern? Fill in the blanks.

Figure 1: 9 cubes
Figure 2: 13 cubes
Figure 3:__17____cubes
Figure 4:__21____cubes
Figure 5:_  25____cubes 

NOTICE HOW:  9+4=131+4=17+4=21+4=25 

EACH TIME, EACH NUMBER GOES UP BY 4!!!

Answer 1

Figure 3: 17 cubes

Figure 4: 21 cubes

Figure 5: 25 cubes

Explanation:

Luis uses cubes to represent each term of a pattern based on a recursive function.

The given recursive function defined as

`f(n+1)=f(n)+4` .... (1)

where n is an integer and n ≥ 2.

It is given

Figure 1: 9 cubes

Figure 2: 13 cubes

`f(1)=9, f(2)=13`

Substitute n=2 in equation (1).

`f(2+1)=f(2)+4`

`f(3)=13+4`

`f(3)=17`

Substitute n=3 in equation (1).

`f(3+1)=f(3)+4`

`f(4)=17+4`

`f(4)=21`

Substitute n=4 in equation (1).

`f(4+1)=f(4)+4`

`f(5)=21+4`

`f(5)=25`

Therefore, the number of cubes in figure 3, 4 and 5 are 17, 21 and 25 respectively.

Answer 2

figure 3: 17 cubes.

figure 4: 21 cubes.

figure 5: 25 cubes.

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.