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Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1? 1, –0.25, –1.5, –2.75, –4, . . . 1, 2.25, 3.5, 4.75, 6, . . . 4, 2.75, 1.5, 0.25, –1, . . . 4, 5.25, 6.5, 7.75, 8, . . .

Respuesta :

Answer:

[tex]4,2.75,1.5,0.25......[/tex]

Step-by-step explanation:

f (1) = 4, [tex]f (n + 1) = f (n) - 1.25[/tex]

To get the sequence we start with n=1

Plug in n=1 in the formula

[tex]f (n + 1) = f (n) - 1.25[/tex]

[tex]f (1 + 1) = f (1) - 1.25[/tex]

[tex]f (2) = f (1) - 1.25[/tex], replace f(1)=4

[tex]f (2) = 4 - 1.25=2.75[/tex]

n=2

[tex]f (2 + 1) = f (2) - 1.25[/tex]

[tex]f (3) = f (2) - 1.25[/tex], replace f(2)=2.75

[tex]f (3) = 2.75 - 1.25=1.5[/tex]

n=3

[tex]f (3 + 1) = f (3) - 1.25[/tex]

[tex]f (4) = f (3) - 1.25[/tex], replace f(3)=1.5

[tex]f (4) = 1.5 - 1.25=0.25[/tex]

Sequence is [tex]4,2.75,1.5,0.25......[/tex]

Answer:

C.

4, 2.75, 1.5, 0.25, –1

Step-by-step explanation:

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