Question

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)

Answer 1

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

Explanation:

Answer 2

`(c)\ f(5) < g(3)`

Explanation:

Given

`f(n) = 2(n-1) -1`

`g(n) = 3n + 6`

Required

Which is correct

`(a)\ g(6) < f(6)`

Calculate g(6) and f(6)

`f(n) = 2(n-1) -1`

`f(6) = 2(6 - 1) -1 = 2*5-1=9`

`g(n) = 3n + 6`

`g(6) =3*6 +6 =24`

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

`(b)\ f(7) > g(10)`

Calculate f(7) and g(10)

`f(n) = 2(n-1) -1`

`f(7) = 2*(7-1)-1=2*6-1=11`

`g(n) = 3n + 6`

`g(10) =3*10+6=36`

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

`(c)\ f(5) < g(3)`

Calculate f(5) and g(3)

`f(n) = 2(n-1) -1`

`f(5) =2 *(5-1)-1 = 2*4-1=7`

`g(n) = 3n + 6`

`g(3) = 3*3+6=9+6=15`

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