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:
figure 4:
figure 5:

2/5

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.