Consider the explicit formulas for two sequences below.

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

g(n)=3n+6

select the correct statement.

a. f(5)< g(3)

b. g(6)> f(6)

c. f(7) > g(10)

d. g(8) = f(5)

C. f(7) > g(10)

Step-by-step explanation:

We are given the explicit formulas as,

and

So, according to the options, we have,

A. f(5) < g(3)

So, i.e. i.e. i.e. f(5) = 15.

And, i.e. i.e. g(3) = 15

Thus, f(5) = g(3).

It is not correct.

B. g(6) > f(6)

So, i.e. i.e. i.e. f(6) = 31

And, i.e. i.e. g(3) = 24

Thus, g(6) < f(6)

It is not correct.

C. f(7) > g(10)

So, i.e. i.e. i.e. f(7) = 63

And, i.e. i.e. g(10) = 36

Thus, f(7)>g(10)

It is correct.

D. g(8) = f(5)

So, i.e. i.e. i.e. f(7) = 15

And, i.e. i.e. g(8) = 30

Thus, g(8) ≠ f(5)

It is not correct.

Thus, the only correct statement is C. f(7) > g(10).

one that is bigger than 3 1/2