Consider the following empty table for an arithmetic sequence defined as $f(n)=12+9(n-1)$ and a geometric sequence defined as $g(n)=$ $64\cdot {\left(\frac{1}{2}\right)}^n$.
a) Arithmetic
b) Geometric
$$\text{Unknown environment 'tabular'}$$
Enter the missing values for row a), in order, separated by a comma.
$12,21,30,39,48$
$12,21,30,39,48$
Enter the missing values for row b), in order, separated by a comma.
Which is the greater value $f(100)$ or $g(100)$ and why?
$f(100)$; because the arithmetic sequence is increasing while the geometric sequence is decreasing.
$g(100)$; because a geometric sequence is multiplying each value which will eventually exceed the addition of an arithmetic sequence.

Step 1 ：Define the arithmetic sequence as $f(n)=12+9(n-1)$ and the geometric sequence as $g(n)=64\cdot {\left(\frac{1}{2}\right)}^n$.

Step 2 ：Calculate the first 5 terms of the arithmetic sequence by substituting the values of n from 1 to 5 into the formula. The results are $12,21,30,39,48$.

Step 3 ：Calculate the first 5 terms of the geometric sequence by substituting the values of n from 1 to 5 into the formula. The results are $32.0,16.0,8.0,4.0,2.0$.

Step 4 ：Calculate the 100th term of both sequences using their respective formulas. The 100th term of the arithmetic sequence is $f(100)=903$ and the 100th term of the geometric sequence is $g(100)=5.048709793414476e-29$.

Step 5 ：Compare the 100th term of both sequences. The greater value is $f(100)$ because $903>5.048709793414476e-29$.

Step 6 ：Final Answer: The missing values for row a) are $\boxed{{\displaystyle 12,21,30,39,48}}$. The missing values for row b) are $\boxed{{\displaystyle 32.0,16.0,8.0,4.0,2.0}}$. The greater value between $f(100)$ and $g(100)$ is $\boxed{{\displaystyle f(100)}}$.