Year 6 maths worksheet: Number sequences (2) - Maths Blog - Free Printable

To solve the problem, we need to identify the next two numbers in each sequence. Let's analyze each sequence step by step.

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Sequence 1:

Numbers: 1, 6, 21, 36, 51, 66, 81, __, __

#### Step 1: Identify the pattern
- The difference between consecutive terms:
- \( 6 - 1 = 5 \)
- \( 21 - 6 = 15 \)
- \( 36 - 21 = 15 \)
- \( 51 - 36 = 15 \)
- \( 66 - 51 = 15 \)
- \( 81 - 66 = 15 \)

The sequence increases by 15 each time.

#### Step 2: Find the next two numbers
- Next number after 81: \( 81 + 15 = 96 \)
- Next number after 96: \( 96 + 15 = 111 \)

#### Final Answer for Sequence 1:
\[ \boxed{96, 111} \]

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Sequence 2:

Numbers: 2, 56, 4, 54, 6, 52, 8, __, __

#### Step 1: Identify the pattern
- The sequence alternates between two patterns:
1. Odd positions (1st, 3rd, 5th, ...): 2, 4, 6, 8, ...
- This is an arithmetic sequence with a common difference of 2.
2. Even positions (2nd, 4th, 6th, ...): 56, 54, 52, ...
- This is an arithmetic sequence with a common difference of -2.

#### Step 2: Find the next two numbers
- Next odd position (after 8): \( 8 + 2 = 10 \)
- Next even position (after 52): \( 52 - 2 = 50 \)

#### Final Answer for Sequence 2:
\[ \boxed{10, 50} \]

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Sequence 3:

Numbers: 3, 7, 11, 15, 19, 23, 27, __, __

#### Step 1: Identify the pattern
- The difference between consecutive terms:
- \( 7 - 3 = 4 \)
- \( 11 - 7 = 4 \)
- \( 15 - 11 = 4 \)
- \( 19 - 15 = 4 \)
- \( 23 - 19 = 4 \)
- \( 27 - 23 = 4 \)

The sequence increases by 4 each time.

#### Step 2: Find the next two numbers
- Next number after 27: \( 27 + 4 = 31 \)
- Next number after 31: \( 31 + 4 = 35 \)

#### Final Answer for Sequence 3:
\[ \boxed{31, 35} \]

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Sequence 4:

Numbers: 4, 24, 8, 20, 12, 16, 16, __, __

#### Step 1: Identify the pattern
- The sequence alternates between two patterns:
1. Odd positions (1st, 3rd, 5th, ...): 4, 8, 12, 16, ...
- This is an arithmetic sequence with a common difference of 4.
2. Even positions (2nd, 4th, 6th, ...): 24, 20, 16, ...
- This is an arithmetic sequence with a common difference of -4.

#### Step 2: Find the next two numbers
- Next odd position (after 16): \( 16 + 4 = 20 \)
- Next even position (after 16): \( 16 - 4 = 12 \)

#### Final Answer for Sequence 4:
\[ \boxed{20, 12} \]

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Sequence 5:

Numbers: 5, 25, 10, 20, 15, 15, 20, __, __

#### Step 1: Identify the pattern
- The sequence alternates between two patterns:
1. Odd positions (1st, 3rd, 5th, ...): 5, 10, 15, 20, ...
- This is an arithmetic sequence with a common difference of 5.
2. Even positions (2nd, 4th, 6th, ...): 25, 20, 15, ...
- This is an arithmetic sequence with a common difference of -5.

#### Step 2: Find the next two numbers
- Next odd position (after 20): \( 20 + 5 = 25 \)
- Next even position (after 15): \( 15 - 5 = 10 \)

#### Final Answer for Sequence 5:
\[ \boxed{25, 10} \]

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Final Answers:

1. \( \boxed{96, 111} \)
2. \( \boxed{10, 50} \)
3. \( \boxed{31, 35} \)
4. \( \boxed{20, 12} \)
5. \( \boxed{25, 10} \)