Given the functions f (n) = 11 and g (n) = (three fourths) n - 1, combine them to create a geometric sequence, an, and solve for the 9th term.

an = (11 • three fourths) n - 1; a9 ≈ 24.301

an = 11 (three fourths) n - 1; a9 ≈ 1.101

an = 11 + (three fourths) n - 1; a9 ≈ 11.100

an = 11 - (three fourths) n - 1; a9 ≈ 9.900

We are given two functions:

f (n) = 11

g (n) = (3/4) ^ (n-1)

I have rewritten the functions to their correct form. Notice that the term (n - 1) is the exponent of 3/4.

We are asked to combine the two functions to model a geometric sequence and solve for the 9th term.

The general formula for a geometric sequence is

an = a1 r^ (n - 1)

From the given functions, we can set

f (n) = a1 = 11

and

g (n) = r^ (n - 1) = (3/4) ^ (n - 1)

Substituting to the general formula of a geometric sequence, the result is

an = 11 (3/4) ^ (n - 1)

Solving for the 9th term

a9 = 11 (3/4) ^ (9 - 1)

a9 = 1.101

The answer is the second option.