Fill in the missing numbers in the number patterns worksheet.

To solve the problem, we need to identify the pattern in each sequence and fill in the missing numbers accordingly. Let's analyze each sequence step by step.

---

Sequence 1:

```
2, 4, 6, _, _, 10, _, 12
```
- The sequence starts with 2.
- The difference between consecutive numbers is 2:
- \(4 - 2 = 2\)
- \(6 - 4 = 2\)
- Following this pattern:
- The next number after 6 is \(6 + 2 = 8\).
- The next number after 8 is \(8 + 2 = 10\) (already given).
- The next number after 10 is \(10 + 2 = 12\) (already given).

So, the completed sequence is:
```
2, 4, 6, 8, 10, 12
```

---

Sequence 2:

```
3, 6, 9, 12, _, 18, _, 24
```
- The sequence starts with 3.
- The difference between consecutive numbers is 3:
- \(6 - 3 = 3\)
- \(9 - 6 = 3\)
- \(12 - 9 = 3\)
- Following this pattern:
- The next number after 12 is \(12 + 3 = 15\).
- The next number after 18 is \(18 + 3 = 21\).

So, the completed sequence is:
```
3, 6, 9, 12, 15, 18, 21, 24
```

---

Sequence 3:

```
4, _, 12, _, 20, 24, _, 32
```
- The sequence starts with 4.
- Observing the given numbers, the difference between some terms is 8:
- \(20 - 12 = 8\)
- \(24 - 20 = 4\) (not consistent, so let's check another pattern).
- Another observation: Each term seems to be a multiple of 4:
- \(4 \times 1 = 4\)
- \(4 \times 3 = 12\)
- \(4 \times 5 = 20\)
- \(4 \times 6 = 24\)
- \(4 \times 8 = 32\)
- Following this pattern:
- The missing term before 12 is \(4 \times 2 = 8\).
- The missing term after 12 is \(4 \times 4 = 16\).
- The missing term after 24 is \(4 \times 7 = 28\).

So, the completed sequence is:
```
4, 8, 12, 16, 20, 24, 28, 32
```

---

Sequence 4:

```
5, 10, _, 20, _, 30, 35, _
```
- The sequence starts with 5.
- Observing the given numbers, the difference between some terms is 5:
- \(10 - 5 = 5\)
- \(20 - 10 = 10\) (not consistent, so let's check another pattern).
- Another observation: Each term seems to increase by multiples of 5:
- \(5 \times 1 = 5\)
- \(5 \times 2 = 10\)
- \(5 \times 4 = 20\)
- \(5 \times 6 = 30\)
- \(5 \times 7 = 35\)
- Following this pattern:
- The missing term after 10 is \(5 \times 3 = 15\).
- The missing term after 20 is \(5 \times 5 = 25\).
- The missing term after 35 is \(5 \times 8 = 40\).

So, the completed sequence is:
```
5, 10, 15, 20, 25, 30, 35, 40
```

---

Sequence 5:

```
_, _, 18, 24, 30, _, 42, 48
```
- The sequence starts with two missing numbers.
- Observing the given numbers, the difference between consecutive terms is 6:
- \(24 - 18 = 6\)
- \(30 - 24 = 6\)
- \(42 - 30 = 12\) (not consistent, but let's check the overall pattern).
- Another observation: Each term seems to increase by 6:
- The term before 18 must be \(18 - 6 = 12\).
- The term before 12 must be \(12 - 6 = 6\).
- The missing term after 30 is \(30 + 6 = 36\).

So, the completed sequence is:
```
6, 12, 18, 24, 30, 36, 42, 48
```

---

Final Answer:

```
1. 2, 4, 6, 8, 10, 12
2. 3, 6, 9, 12, 15, 18, 21, 24
3. 4, 8, 12, 16, 20, 24, 28, 32
4. 5, 10, 15, 20, 25, 30, 35, 40
5. 6, 12, 18, 24, 30, 36, 42, 48
```

\boxed{
\begin{aligned}
&1. 2, 4, 6, 8, 10, 12 \\
&2. 3, 6, 9, 12, 15, 18, 21, 24 \\
&3. 4, 8, 12, 16, 20, 24, 28, 32 \\
&4. 5, 10, 15, 20, 25, 30, 35, 40 \\
&5. 6, 12, 18, 24, 30, 36, 42, 48
\end{aligned}
}