Question

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

Answer 1

Answer:

f(2)=5

f(5)=33

Step-by-step explanation:

The given formula, that recursively defines the sequence is

$f(1) = 3 \\ f(n + 1) = 2f(n) - 1$

When n=1, we obtain;

$f(1+ 1) = 2f(1) - 1 \\ f(2) = 2 \times 3 - 1 \\ f(2) = 6 - 1 \\ f(2) = 5$

When n=2, we get:

$f(2+ 1) = 2f(2) - 1 \\ f(3) = 2 \times 5 - 1 \\ f(3) = 10 - 1 \\ f(3) = 9$

When n=3,

$f(3 + 1) = 2f(3) - 1 \\ f(4) = 2f(3) - 1 \\ f(4) = 2 \times 9 - 1 \\ f(4) = 18 - 1 \\ f(4) = 17$

When n=4

$f(4 + 1) = 2 f(4) - 1 \\ f(5) = 2 \times 17 - 1 \\ f(5) = 34 - 1 \\ f(5) = 33$

When n=5,

$f(6) = 65$