Consider the arithmetic sequence -11, -8, -5, -2, ... Find the next three terms and the formula for the nth term.

Okay, let's tackle the second pattern from your image.

The given number pattern is $-11, -8, -5, -2, \dots$

Step 1: Find the common difference.
The difference between consecutive terms is:
$-8 - (-11) = -8 + 11 = 3$
$-5 - (-8) = -5 + 8 = 3$
$-2 - (-5) = -2 + 5 = 3$
The common difference is $d=3$.

2.1 Write down the next three terms if the pattern continues in the same way.
To find the next terms, add the common difference to the last known term.
The last given term is $-2$.
Next term: $-2 + 3 = 1$
Next term: $1 + 3 = 4$
Next term: $4 + 3 = 7$
The next three terms are $\boxed{1, 4, 7}$.

2.2 If the pattern continues in the same way, write a formula for the $n^{th}$ term in the form $T_n = \dots$.
For an arithmetic sequence, the formula for the $n^{th}$ term is $T_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.
Here, $a=-11$ and $d=3$.
Substitute these values into the formula:

$$T_n = -11 + (n-1)3$$ $$T_n = -11 + 3n - 3$$ $$T_n = 3n - 14$$

The formula for the $n^{th}$ term is $\boxed{T_n = 3n - 14}$.