Complete the number patterns in this Grade 7 math worksheet from Smart-Kids.

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

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1. 2; 6; 9; 12; ...

- Pattern: The differences between consecutive terms are:
- \(6 - 2 = 4\)
- \(9 - 6 = 3\)
- \(12 - 9 = 3\)
- It appears that the sequence alternates between adding 4 and adding 3.
- Continuing the pattern:
- Next term: \(12 + 4 = 16\)
- Next term: \(16 + 3 = 19\)
- Completed sequence: \(2; 6; 9; 12; 16; 19\)

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2. 33; 41; 51; ...

- Pattern: The differences between consecutive terms are:
- \(41 - 33 = 8\)
- \(51 - 41 = 10\)
- The differences increase by 2 each time (8, 10, 12, ...).
- Continuing the pattern:
- Next term: \(51 + 12 = 63\)
- Next term: \(63 + 14 = 77\)
- Completed sequence: \(33; 41; 51; 63; 77\)

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3. 18; 27; 36; ...

- Pattern: Each term increases by 9.
- \(27 - 18 = 9\)
- \(36 - 27 = 9\)
- Continuing the pattern:
- Next term: \(36 + 9 = 45\)
- Next term: \(45 + 9 = 54\)
- Completed sequence: \(18; 27; 36; 45; 54\)

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4. 0; 0.5; 0.7; ...

- Pattern: The sequence appears to involve decimal increments.
- From \(0\) to \(0.5\): Increase by \(0.5\)
- From \(0.5\) to \(0.7\): Increase by \(0.2\)
- The increments seem to decrease by \(0.3\) each time (\(0.5, 0.2, -0.1, \ldots\)).
- Continuing the pattern:
- Next term: \(0.7 + (-0.1) = 0.6\)
- Next term: \(0.6 + (-0.4) = 0.2\)
- Completed sequence: \(0; 0.5; 0.7; 0.6; 0.2\)

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5. 12%; 20%; 28%; ...

- Pattern: Each term increases by \(8\%\).
- \(20\% - 12\% = 8\%\)
- \(28\% - 20\% = 8\%\)
- Continuing the pattern:
- Next term: \(28\% + 8\% = 36\%\)
- Next term: \(36\% + 8\% = 44\%\)
- Completed sequence: \(12\%; 20\%; 28\%; 36\%; 44\%\)

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6. 1.2; 1.8; 2.4; ...

- Pattern: Each term increases by \(0.6\).
- \(1.8 - 1.2 = 0.6\)
- \(2.4 - 1.8 = 0.6\)
- Continuing the pattern:
- Next term: \(2.4 + 0.6 = 3.0\)
- Next term: \(3.0 + 0.6 = 3.6\)
- Completed sequence: \(1.2; 1.8; 2.4; 3.0; 3.6\)

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7. 784; 786; 792; 802; ...

- Pattern: The differences between consecutive terms are:
- \(786 - 784 = 2\)
- \(792 - 786 = 6\)
- \(802 - 792 = 10\)
- The differences increase by \(4\) each time (\(2, 6, 10, 14, \ldots\)).
- Continuing the pattern:
- Next term: \(802 + 14 = 816\)
- Next term: \(816 + 18 = 834\)
- Completed sequence: \(784; 786; 792; 802; 816; 834\)

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8. 81; 83; 85; 87; ...

- Pattern: Each term increases by \(2\).
- \(83 - 81 = 2\)
- \(85 - 83 = 2\)
- \(87 - 85 = 2\)
- Continuing the pattern:
- Next term: \(87 + 2 = 89\)
- Next term: \(89 + 2 = 91\)
- Completed sequence: \(81; 83; 85; 87; 89; 91\)

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9. 16; 25; 36; 49; ...

- Pattern: These are perfect squares of consecutive integers.
- \(16 = 4^2\)
- \(25 = 5^2\)
- \(36 = 6^2\)
- \(49 = 7^2\)
- Continuing the pattern:
- Next term: \(8^2 = 64\)
- Next term: \(9^2 = 81\)
- Completed sequence: \(16; 25; 36; 49; 64; 81\)

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10. 1/3; 1/3; 1/3; 1/3; ...

- Pattern: All terms are the same (\(1/3\)).
- Continuing the pattern:
- Next term: \(1/3\)
- Next term: \(1/3\)
- Completed sequence: \(1/3; 1/3; 1/3; 1/3; 1/3; 1/3\)

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11. 945; 925; 905; ...

- Pattern: Each term decreases by \(20\).
- \(925 - 945 = -20\)
- \(905 - 925 = -20\)
- Continuing the pattern:
- Next term: \(905 - 20 = 885\)
- Next term: \(885 - 20 = 865\)
- Completed sequence: \(945; 925; 905; 885; 865\)

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12. 1.3; 1.6; 1.9; ...

- Pattern: Each term increases by \(0.3\).
- \(1.6 - 1.3 = 0.3\)
- \(1.9 - 1.6 = 0.3\)
- Continuing the pattern:
- Next term: \(1.9 + 0.3 = 2.2\)
- Next term: \(2.2 + 0.3 = 2.5\)
- Completed sequence: \(1.3; 1.6; 1.9; 2.2; 2.5\)

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13. 84; 72; 60; ...

- Pattern: Each term decreases by \(12\).
- \(72 - 84 = -12\)
- \(60 - 72 = -12\)
- Continuing the pattern:
- Next term: \(60 - 12 = 48\)
- Next term: \(48 - 12 = 36\)
- Completed sequence: \(84; 72; 60; 48; 36\)

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14. -6; -3; -1; 0; ...

- Pattern: The differences between consecutive terms are:
- \(-3 - (-6) = 3\)
- \(-1 - (-3) = 2\)
- \(0 - (-1) = 1\)
- The differences decrease by \(1\) each time (\(3, 2, 1, 0, \ldots\)).
- Continuing the pattern:
- Next term: \(0 + 0 = 0\)
- Next term: \(0 + 1 = 1\)
- Completed sequence: \(-6; -3; -1; 0; 0; 1\)

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15. 7; 9; 27; 31; ...

- Pattern: This sequence is more complex. Let's break it down:
- \(9 - 7 = 2\)
- \(27 - 9 = 18\)
- \(31 - 27 = 4\)
- The differences are \(2, 18, 4\). This does not immediately suggest a simple arithmetic or geometric pattern. However, if we look at the sequence as groups:
- First group: \(7, 9\) (difference = 2)
- Second group: \(27, 31\) (difference = 4)
- It seems the sequence alternates between small and large jumps. Assuming the pattern continues:
- Next term: \(31 + 6 = 37\) (next jump could be \(6\))
- Next term: \(37 + 18 = 55\) (next large jump could be \(18\))
- Completed sequence: \(7; 9; 27; 31; 37; 55\)

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Final Answer

\[
\boxed{
\begin{array}{l}
1. 2; 6; 9; 12; 16; 19 \\
2. 33; 41; 51; 63; 77 \\
3. 18; 27; 36; 45; 54 \\
4. 0; 0.5; 0.7; 0.6; 0.2 \\
5. 12\%; 20\%; 28\%; 36\%; 44\% \\
6. 1.2; 1.8; 2.4; 3.0; 3.6 \\
7. 784; 786; 792; 802; 816; 834 \\
8. 81; 83; 85; 87; 89; 91 \\
9. 16; 25; 36; 49; 64; 81 \\
10. 1/3; 1/3; 1/3; 1/3; 1/3; 1/3 \\
11. 945; 925; 905; 885; 865 \\
12. 1.3; 1.6; 1.9; 2.2; 2.5 \\
13. 84; 72; 60; 48; 36 \\
14. -6; -3; -1; 0; 0; 1 \\
15. 7; 9; 27; 31; 37; 55 \\
\end{array}
}
\]