Count in Steps of 6, 7 and 9 worksheet with sequence completion exercises and an eco-friendly ink-saving design.

Problem Overview:

The task involves completing sequences by counting in steps of 6, 7, and 9. The goal is to identify the missing numbers in each sequence based on the given step size.

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Solution:

#### Part 1: Counting in Steps of 6, 7, and 9

##### a) Sequence: \( \_, 12, 18, 24, 30, \_ \)
- The sequence increases by 6 (step of 6).
- Missing first number: \( 12 - 6 = 6 \).
- Missing last number: \( 30 + 6 = 36 \).
- Answer: \( 6, 12, 18, 24, 30, 36 \).

##### b) Sequence: \( 4, 9, \_, 28, 14 \)
- This sequence does not follow a consistent step of 6, 7, or 9. It appears to be irregular. Let's analyze it further.
- The difference between 9 and 4 is 5, and the difference between 28 and 9 is 19. This sequence does not fit the given instructions. Assuming it was meant to be a step of 7:
- Missing number: \( 9 + 7 = 16 \).
- Answer (assuming step of 7): \( 4, 9, 16, 28, 14 \).

##### c) Sequence: \( 45, 54, 63, \_, 81 \)
- The sequence increases by 9 (step of 9).
- Missing number: \( 63 + 9 = 72 \).
- Answer: \( 45, 54, 63, 72, 81 \).

##### d) Sequence: \( 90, \_, 72, 66, 60 \)
- The sequence decreases by 6 (step of -6).
- Missing number: \( 90 - 6 = 84 \).
- Answer: \( 90, 84, 72, 66, 60 \).

##### e) Sequence: \( 56, \_, 70, 77, 91 \)
- The sequence increases by 7 (step of 7).
- Missing number: \( 56 + 7 = 63 \).
- Answer: \( 56, 63, 70, 77, 91 \).

##### f) Sequence: \( \_, 126, 120, 108, 102 \)
- The sequence decreases by 6 (step of -6).
- Missing first number: \( 126 + 6 = 132 \).
- Answer: \( 132, 126, 120, 108, 102 \).

##### g) Sequence: \( 99, 108, \_, 126, 144 \)
- The sequence increases by 9 (step of 9).
- Missing number: \( 108 + 9 = 117 \).
- Answer: \( 99, 108, 117, 126, 144 \).

##### h) Sequence: \( 112, 126, \_, 133, 140 \)
- The sequence increases by 7 (step of 7).
- Missing number: \( 126 + 7 = 133 \). However, 133 is already in the sequence, so the pattern might be irregular. Assuming it's a step of 7:
- Missing number: \( 126 + 7 = 133 \) (already present, so no change).
- Answer: \( 112, 126, 133, 133, 140 \).

##### i) Sequence: \( \_, 183, 186, 192, 198 \)
- The sequence increases by 3 (step of 3), but this does not match the instructions. Assuming it was meant to be a step of 9:
- Missing number: \( 183 - 9 = 174 \).
- Answer (assuming step of 9): \( 174, 183, 186, 192, 198 \).

##### j) Sequence: \( 210, 203, \_, 189, 175 \)
- The sequence decreases by 7 (step of -7).
- Missing number: \( 203 - 7 = 196 \).
- Answer: \( 210, 203, 196, 189, 175 \).

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#### Part 2: Complete the following sequences

##### k) Sequence: \( 35, 41, 47, \_, \_, \_, \_, \_, \_ \)
- The sequence increases by 6 (step of 6).
- Missing numbers: \( 47 + 6 = 53 \), \( 53 + 6 = 59 \), \( 59 + 6 = 65 \), \( 65 + 6 = 71 \), \( 71 + 6 = 77 \).
- Answer: \( 35, 41, 47, 53, 59, 65, 71, 77 \).

##### l) Sequence: \( 2, 11, 20, \_, \_, \_, \_, \_, \_ \)
- The sequence increases by 9 (step of 9).
- Missing numbers: \( 20 + 9 = 29 \), \( 29 + 9 = 38 \), \( 38 + 9 = 47 \), \( 47 + 9 = 56 \), \( 56 + 9 = 65 \).
- Answer: \( 2, 11, 20, 29, 38, 47, 56, 65 \).

##### m) Sequence: \( 40, 47, 54, \_, \_, \_, \_, \_, \_ \)
- The sequence increases by 7 (step of 7).
- Missing numbers: \( 54 + 7 = 61 \), \( 61 + 7 = 68 \), \( 68 + 7 = 75 \), \( 75 + 7 = 82 \), \( 82 + 7 = 89 \).
- Answer: \( 40, 47, 54, 61, 68, 75, 82, 89 \).

##### n) Sequence: \( 100, 106, 112, \_, \_, \_, \_, \_, \_ \)
- The sequence increases by 6 (step of 6).
- Missing numbers: \( 112 + 6 = 118 \), \( 118 + 6 = 124 \), \( 124 + 6 = 130 \), \( 130 + 6 = 136 \), \( 136 + 6 = 142 \).
- Answer: \( 100, 106, 112, 118, 124, 130, 136, 142 \).

##### o) Sequence: \( 99, 106, 113, \_, \_, \_, \_, \_, \_ \)
- The sequence increases by 7 (step of 7).
- Missing numbers: \( 113 + 7 = 120 \), \( 120 + 7 = 127 \), \( 127 + 7 = 134 \), \( 134 + 7 = 141 \), \( 141 + 7 = 148 \).
- Answer: \( 99, 106, 113, 120, 127, 134, 141, 148 \).

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a)} & 6, 12, 18, 24, 30, 36 \\
\text{b)} & 4, 9, 16, 28, 14 \\
\text{c)} & 45, 54, 63, 72, 81 \\
\text{d)} & 90, 84, 72, 66, 60 \\
\text{e)} & 56, 63, 70, 77, 91 \\
\text{f)} & 132, 126, 120, 108, 102 \\
\text{g)} & 99, 108, 117, 126, 144 \\
\text{h)} & 112, 126, 133, 133, 140 \\
\text{i)} & 174, 183, 186, 192, 198 \\
\text{j)} & 210, 203, 196, 189, 175 \\
\text{k)} & 35, 41, 47, 53, 59, 65, 71, 77 \\
\text{l)} & 2, 11, 20, 29, 38, 47, 56, 65 \\
\text{m)} & 40, 47, 54, 61, 68, 75, 82, 89 \\
\text{n)} & 100, 106, 112, 118, 124, 130, 136, 142 \\
\text{o)} & 99, 106, 113, 120, 127, 134, 141, 148 \\
\end{array}
}
\]