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Select the correct answer.
Consider the explicit formulas for two sequences.
f(n) = 2(1 – 1) - 1
g(n) = 3n + 6
Which mathematical statement is correct?
O A. 96) > 6)
O B. (7) > g(10)
OC. F(5) < g(3)
O D.g(8) = f(5)

Respuesta :

MrRoyal

Answer:

[tex](c)\ f(5) < g(3)[/tex]

Step-by-step explanation:

Given

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

[tex]g(n) = 3n + 6[/tex]

Required

Which is correct

[tex](a)\ g(6) < f(6)[/tex]

Calculate g(6) and f(6)

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

[tex]f(6) = 2(6 - 1) -1 = 2*5-1=9[/tex]

[tex]g(n) = 3n + 6[/tex]

[tex]g(6) =3*6 +6 =24[/tex]

(a) is false, because g(6) > f(6) i.e. 24 > 9

[tex](b)\ f(7) > g(10)[/tex]

Calculate f(7) and g(10)

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

[tex]f(7) = 2*(7-1)-1=2*6-1=11[/tex]

[tex]g(n) = 3n + 6[/tex]

[tex]g(10) =3*10+6=36[/tex]

(b) is false, because f(7) < g(10) i.e. 11 <36

[tex](c)\ f(5) < g(3)[/tex]

Calculate f(5) and g(3)

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

[tex]f(5) =2 *(5-1)-1 = 2*4-1=7[/tex]

[tex]g(n) = 3n + 6[/tex]

[tex]g(3) = 3*3+6=9+6=15[/tex]

(c) is true, because f(5) < g(3) i.e. 7 <15

Answer:

the answer is f(7) > g(10) because 63 > 36.

Step-by-step explanation:

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