contestada

1. Which formula defines the sequence f(1)=2, f(2)= 6, f(3)= 10, f(4)= 14, f(5)= 18?
A. 101- 2. f(n)= 6 + f(n-1) for n> 2
B. f(1)= 2, f(n)= 4 fln-1) for n> 2
C. f(1)= 2, f(n)= 2 + f(n-1) for n 2
D. f(1)= 6, f(n)= 4 + f(n-1) for n> 2
А
B
С
D

Respuesta :

MrRoyal

Answer:

[tex]f(n) =4 + f(n-1) \\for\ n>2[/tex]

Step-by-step explanation:

Given

[tex]f(1)=2\\ f(2)= 6\\ f(3)= 10\\ f(4)= 14\\ f(5)= 18[/tex]

Required

Determine the formula

First, we need to solve common difference (d)

[tex]d = f(n) - f(n-1)[/tex]

Take n as 2

[tex]d = f(2) - f(2-1)[/tex]

[tex]d = 6 - 2[/tex]

[tex]d = 4[/tex]

Represent each function as a sum of the previous

[tex]f(1) = 2[/tex]

[tex]f(2) = 2 + 4 = f(1) + 4[/tex]

[tex]f(3) = 6 + 4 = f(2) + 4[/tex]

[tex]f(4) = 10 + 4 = f(3) + 4[/tex]

[tex]f(5) = 14 + 4 = f(4) + 4[/tex]

Represent the function as [tex]f(n)[/tex]

[tex]f(n) =f(n-1) + 4[/tex]

Reorder

[tex]f(n) =4 + f(n-1) \\for\ n>2[/tex]

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