Number pattern worksheets for practicing sequence recognition and pattern description.

Let's solve each sequence step by step and describe the pattern.

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Sequence 1:

$$
3, 6, 9, 12, 15, 18, \_\_
$$

#### Step 1: Identify the Pattern
- The sequence starts with 3.
- Each term increases by 3:
- \( 3 + 3 = 6 \)
- \( 6 + 3 = 9 \)
- \( 9 + 3 = 12 \)
- \( 12 + 3 = 15 \)
- \( 15 + 3 = 18 \)

#### Step 2: Find the Next Term
- The next term is:
$$
18 + 3 = 21
$$

#### Step 3: Describe the Pattern
- The sequence is an arithmetic progression where each term increases by 3.

#### Final Answer for Sequence 1:
$$
\boxed{21}
$$

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Sequence 2:

$$
20, 18, 16, 14, 12, 10, \_\_
$$

#### Step 1: Identify the Pattern
- The sequence starts with 20.
- Each term decreases by 2:
- \( 20 - 2 = 18 \)
- \( 18 - 2 = 16 \)
- \( 16 - 2 = 14 \)
- \( 14 - 2 = 12 \)
- \( 12 - 2 = 10 \)

#### Step 2: Find the Next Term
- The next term is:
$$
10 - 2 = 8
$$

#### Step 3: Describe the Pattern
- The sequence is an arithmetic progression where each term decreases by 2.

#### Final Answer for Sequence 2:
$$
\boxed{8}
$$

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Sequence 3:

$$
2, 2, 6, 6, 8, 8, \_\_, \_\_
$$

#### Step 1: Identify the Pattern
- The sequence alternates between repeating numbers:
- The first two terms are \( 2, 2 \).
- The next two terms are \( 6, 6 \).
- The next two terms are \( 8, 8 \).

#### Step 2: Determine the Next Pair
- The pattern suggests that the next pair of numbers will be the same as the previous pairs but increasing by a consistent difference.
- Observing the differences:
- \( 6 - 2 = 4 \)
- \( 8 - 6 = 2 \)
- The differences alternate between 4 and 2. The next difference should be 4 (since the last difference was 2):
$$
8 + 4 = 12
$$
- Therefore, the next pair is \( 12, 12 \).

#### Step 3: Describe the Pattern
- The sequence alternates between repeating numbers, with the repeated numbers increasing by alternating differences of 4 and 2.

#### Final Answer for Sequence 3:
$$
\boxed{12, 12}
$$

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Summary of Answers:

1. \( \boxed{21} \)
2. \( \boxed{8} \)
3. \( \boxed{12, 12} \)