Study the number pattern below and answer the questions that follow. $$ -11 ;-16 ;-21 ; \ldots . $$ 4.2.1. Write down the next three terms in the sequence. 4.2.2. Determine the general rule ( $$ n n^{*} $$ term) of the given sequence.

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To analyze the number pattern given:

$$ -11, -16, -21, \ldots $$

### Step 1: Identify the pattern

Let's look at the differences between consecutive terms:

- The difference between the first term (-11) and the second term (-16) is:
  $$
  -16 - (-11) = -16 + 11 = -5
  $$

- The difference between the second term (-16) and the third term (-21) is:
  $$
  -21 - (-16) = -21 + 16 = -5
  $$

The difference between each term is consistently $$-5$$. This indicates that the sequence is an arithmetic sequence with a common difference of $$-5$$.

### Step 2: Write down the next three terms

To find the next three terms, we continue subtracting $$5$$ from the last term:

1. Fourth term:
   $$
   -21 - 5 = -26
   $$

2. Fifth term:
   $$
   -26 - 5 = -31
   $$

3. Sixth term:
   $$
   -31 - 5 = -36
   $$

Thus, the next three terms in the sequence are:
$$
-26, -31, -36
$$

### Step 3: Determine the general rule ( $$ n^{*} $$ term)

In an arithmetic sequence, the $$ n^{*} $$ term can be expressed as:
$$
a_n = a_1 + (n - 1) \cdot d
$$
where:
- $$ a_1 $$ is the first term,
- $$ d $$ is the common difference,
- $$ n $$ is the term number.

For this sequence:
- $$ a_1 = -11 $$
- $$ d = -5 $$

Substituting these values into the formula gives:
$$
a_n = -11 + (n - 1)(-5)
$$

Now, simplifying this expression:
$$
a_n = -11 - 5(n - 1)
$$
$$
a_n = -11 - 5n + 5
$$
$$
a_n = -5n - 6
$$

### Final Answers

4.2.1. The next three terms in the sequence are:
$$
-26, -31, -36
$$

4.2.2. The general rule ( $$ n^{*} $$ term) of the given sequence is:
$$
a_n = -5n - 6
$$
The next three terms are -26, -31, and -36. The general rule for the $$ n^{*} $$ term is $$ a_n = -5n - 6 $$.

Study the number pattern below and answer the questions that follow. \[ -11 ;-16 ;-21 ; \ldots . \] 4.2.1. Write down the next three terms in the sequence. 4.2.2. Determine the general rule ( \( n n^{*} \) term) of the given sequence.

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