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A sequence is defined recursively by the following rules: f(1)=3f(n+1)=2⋅f(n)−1 Which of the following statements is true about the sequence?
Select all that apply.
f(2)=5
f(6)=66
f(3)=10
f(4)=18
f(5)=33

Respuesta :

kudzordzifrancis

Answer:

f(2)=5

f(5)=33

Step-by-step explanation:

The given formula, that recursively defines the sequence is

[tex]f(1) = 3 \\ f(n + 1) = 2f(n) - 1[/tex]

When n=1, we obtain;

[tex]f(1+ 1) = 2f(1) - 1 \\ f(2) = 2 \times 3 - 1 \\ f(2) = 6 - 1 \\ f(2) = 5[/tex]

When n=2, we get:

[tex]f(2+ 1) = 2f(2) - 1 \\ f(3) = 2 \times 5 - 1 \\ f(3) = 10 - 1 \\ f(3) = 9[/tex]

When n=3,

[tex]f(3 + 1) = 2f(3) - 1 \\ f(4) = 2f(3) - 1 \\ f(4) = 2 \times 9 - 1 \\ f(4) = 18 - 1 \\ f(4) = 17[/tex]

When n=4

[tex]f(4 + 1) = 2 f(4) - 1 \\ f(5) = 2 \times 17 - 1 \\ f(5) = 34 - 1 \\ f(5) = 33[/tex]

When n=5,

[tex]f(6) = 65[/tex]

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