Find the rule for the sequence: Input (n): 1, 2, 3, 4. Output (Tn): 7, 9, 11, 13. Then find the 10th and 100th terms.

We are given the input and output values for :
Input ($n$): 1, 2, 3, 4
Output ($T_n$): 7, 9, 11, 13

First, find the common difference between consecutive output values:
$9 - 7 = 2$
$11 - 9 = 2$
$13 - 11 = 2$
The common difference is 2. This indicates a linear rule of the form $T_n = an + b$, where $a$ is the common difference.
So, $a = 2$. The rule is $T_n = 2n + b$.

Substitute one of the input-output pairs into the rule. Using $n=1$ and $T_1=7$:

$$7 = 2(1) + b$$ $$7 = 2 + b$$ $$b = 7 - 2$$ $$b = 5$$

The rule for the sequence is $T_n = 2n + 5$.

For Input $n=10$:

$$T_{10} = 2(10) + 5 = 20 + 5 = 25$$

For Input $n=100$:

$$T_{100} = 2(100) + 5 = 200 + 5 = 205$$

The rule is: $\boxed{T_n = 2n + 5}$

The completed table is:

Input	1	2	3	4	10	100
Output	7	9	11	13	25	205

The terms are:
$T_1 = \boxed{7}$
$T_2 = \boxed{9}$
$T_3 = \boxed{11}$
$T_4 = \boxed{13}$
$T_{10} = \boxed{25}$
$T_{100} = \boxed{205}$