Identifying number patterns, numbers up to 60 | 3rd grade, 4th ... - Free Printable

To solve the problem of identifying patterns in the given image, we need to carefully analyze each sequence and determine the underlying rules. Let's break it down step by step.

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Task 1: Continue each pattern (Intervals of 2)

The sequences are:
1. \(0, 10, 20, \_\_, \_\_, \_\_\)
2. \(15, 25, \_\_, \_\_, \_\_\)
3. \(1, 3, 5, \_\_, \_\_, \_\_\)
4. \(2, 9, 16, \_\_, \_\_, \_\_\)
5. \(4, 7, 10, \_\_, \_\_, \_\_\)
6. \(2, 12, 18, \_\_, \_\_, \_\_\)

#### Solution:
- Sequence 1: \(0, 10, 20, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(10\).
- Next terms: \(20 + 10 = 30\), \(30 + 10 = 40\), \(40 + 10 = 50\).
- Answer: \(0, 10, 20, 30, 40, 50\).

- Sequence 2: \(15, 25, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(10\).
- Next terms: \(25 + 10 = 35\), \(35 + 10 = 45\), \(45 + 10 = 55\).
- Answer: \(15, 25, 35, 45, 55\).

- Sequence 3: \(1, 3, 5, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(2\).
- Next terms: \(5 + 2 = 7\), \(7 + 2 = 9\), \(9 + 2 = 11\).
- Answer: \(1, 3, 5, 7, 9, 11\).

- Sequence 4: \(2, 9, 16, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(7\).
- Next terms: \(16 + 7 = 23\), \(23 + 7 = 30\), \(30 + 7 = 37\).
- Answer: \(2, 9, 16, 23, 30, 37\).

- Sequence 5: \(4, 7, 10, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(3\).
- Next terms: \(10 + 3 = 13\), \(13 + 3 = 16\), \(16 + 3 = 19\).
- Answer: \(4, 7, 10, 13, 16, 19\).

- Sequence 6: \(2, 12, 18, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(10\) and \(6\), but this does not follow a simple arithmetic progression. Let's re-evaluate.
- Upon closer inspection, the sequence might involve a different rule (e.g., multiplication or another pattern). However, based on the provided intervals, let's assume the next term follows a similar pattern.
- Next terms: \(18 + 10 = 28\), \(28 + 6 = 34\), \(34 + 10 = 44\).
- Answer: \(2, 12, 18, 28, 34, 44\).

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Task 2: Continue each pattern (Intervals of 3)

The sequences are:
1. \(64, 38, 32, \_\_, \_\_, \_\_ \)
2. \(33, 29, 25, \_\_, \_\_, \_\_ \)
3. \(21, 27, 33, \_\_, \_\_, \_\_ \)
4. \(56, 48, 45, \_\_, \_\_, \_\_ \)
5. \(89, 42, 35, \_\_, \_\_, \_\_ \)
6. \(28, 25, 22, \_\_, \_\_, \_\_ \)

#### Solution:
- Sequence 1: \(64, 38, 32, \_\_, \_\_, \_\_ \)
- The differences are not consistent (\(64 - 38 = 26\), \(38 - 32 = 6\)). This might involve a different rule.
- Assuming a decreasing pattern with intervals of 3: \(32 - 3 = 29\), \(29 - 3 = 26\), \(26 - 3 = 23\).
- Answer: \(64, 38, 32, 29, 26, 23\).

- Sequence 2: \(33, 29, 25, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(4\).
- Next terms: \(25 - 4 = 21\), \(21 - 4 = 17\), \(17 - 4 = 13\).
- Answer: \(33, 29, 25, 21, 17, 13\).

- Sequence 3: \(21, 27, 33, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(6\).
- Next terms: \(33 + 6 = 39\), \(39 + 6 = 45\), \(45 + 6 = 51\).
- Answer: \(21, 27, 33, 39, 45, 51\).

- Sequence 4: \(56, 48, 45, \_\_, \_\_, \_\_ \)
- The differences are not consistent (\(56 - 48 = 8\), \(48 - 45 = 3\)). This might involve a different rule.
- Assuming a decreasing pattern with intervals of 3: \(45 - 3 = 42\), \(42 - 3 = 39\), \(39 - 3 = 36\).
- Answer: \(56, 48, 45, 42, 39, 36\).

- Sequence 5: \(89, 42, 35, \_\_, \_\_, \_\_ \)
- The differences are not consistent (\(89 - 42 = 47\), \(42 - 35 = 7\)). This might involve a different rule.
- Assuming a decreasing pattern with intervals of 3: \(35 - 3 = 32\), \(32 - 3 = 29\), \(29 - 3 = 26\).
- Answer: \(89, 42, 35, 32, 29, 26\).

- Sequence 6: \(28, 25, 22, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(3\).
- Next terms: \(22 - 3 = 19\), \(19 - 3 = 16\), \(16 - 3 = 13\).
- Answer: \(28, 25, 22, 19, 16, 13\).

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Task 3: Continue each pattern

The sequences are:
1. \(36, 32, 26, 12, \_\_, \_\_, \_\_ \)
2. \(5, 14, 23, \_\_, \_\_, \_\_ \)
3. \(8, 18, 28, \_\_, \_\_, \_\_ \)
4. \(67, 62, 53, \_\_, \_\_, \_\_ \)
5. \(1, 4, 7, \_\_, \_\_, \_\_ \)

#### Solution:
- Sequence 1: \(36, 32, 26, 12, \_\_, \_\_, \_\_ \)
- The differences are not consistent (\(36 - 32 = 4\), \(32 - 26 = 6\), \(26 - 12 = 14\)). This might involve a different rule.
- Assuming a decreasing pattern with intervals of 3: \(12 - 3 = 9\), \(9 - 3 = 6\), \(6 - 3 = 3\).
- Answer: \(36, 32, 26, 12, 9, 6, 3\).

- Sequence 2: \(5, 14, 23, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(9\).
- Next terms: \(23 + 9 = 32\), \(32 + 9 = 41\), \(41 + 9 = 50\).
- Answer: \(5, 14, 23, 32, 41, 50\).

- Sequence 3: \(8, 18, 28, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(10\).
- Next terms: \(28 + 10 = 38\), \(38 + 10 = 48\), \(48 + 10 = 58\).
- Answer: \(8, 18, 28, 38, 48, 58\).

- Sequence 4: \(67, 62, 53, \_\_, \_\_, \_\_ \)
- The differences are not consistent (\(67 - 62 = 5\), \(62 - 53 = 9\)). This might involve a different rule.
- Assuming a decreasing pattern with intervals of 3: \(53 - 3 = 50\), \(50 - 3 = 47\), \(47 - 3 = 44\).
- Answer: \(67, 62, 53, 50, 47, 44\).

- Sequence 5: \(1, 4, 7, \_\_, \_\_, \_\_ \)
- The difference between consecutive terms is \(3\).
- Next terms: \(7 + 3 = 10\), \(10 + 3 = 13\), \(13 + 3 = 16\).
- Answer: \(1, 4, 7, 10, 13, 16\).

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Final Answers:

1. Intervals of 2:
- \(0, 10, 20, 30, 40, 50\)
- \(15, 25, 35, 45, 55\)
- \(1, 3, 5, 7, 9, 11\)
- \(2, 9, 16, 23, 30, 37\)
- \(4, 7, 10, 13, 16, 19\)
- \(2, 12, 18, 28, 34, 44\)

2. Intervals of 3:
- \(64, 38, 32, 29, 26, 23\)
- \(33, 29, 25, 21, 17, 13\)
- \(21, 27, 33, 39, 45, 51\)
- \(56, 48, 45, 42, 39, 36\)
- \(89, 42, 35, 32, 29, 26\)
- \(28, 25, 22, 19, 16, 13\)

3. Continue each pattern:
- \(36, 32, 26, 12, 9, 6, 3\)
- \(5, 14, 23, 32, 41, 50\)
- \(8, 18, 28, 38, 48, 58\)
- \(67, 62, 53, 50, 47, 44\)
- \(1, 4, 7, 10, 13, 16\)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Intervals of 2:} \\
0, 10, 20, 30, 40, 50 \\
15, 25, 35, 45, 55 \\
1, 3, 5, 7, 9, 11 \\
2, 9, 16, 23, 30, 37 \\
4, 7, 10, 13, 16, 19 \\
2, 12, 18, 28, 34, 44 \\
\\
\text{Intervals of 3:} \\
64, 38, 32, 29, 26, 23 \\
33, 29, 25, 21, 17, 13 \\
21, 27, 33, 39, 45, 51 \\
56, 48, 45, 42, 39, 36 \\
89, 42, 35, 32, 29, 26 \\
28, 25, 22, 19, 16, 13 \\
\\
\text{Continue each pattern:} \\
36, 32, 26, 12, 9, 6, 3 \\
5, 14, 23, 32, 41, 50 \\
8, 18, 28, 38, 48, 58 \\
67, 62, 53, 50, 47, 44 \\
1, 4, 7, 10, 13, 16 \\
\end{array}
}
\]