Number Patterns worksheet for 4th grade students to practice identifying and completing sequences using addition and subtraction rules.

Let’s solve each part step by step.

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Part 1: Complete each pattern

We are given starting numbers and rules to add or subtract. We’ll apply the rule repeatedly to fill in the blanks.

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Pattern 1: Start at 17, add 4 each time

- 17 + 4 = 21
- 21 + 4 = 25
- 25 + 4 = 29
- 29 + 4 = 33
- 33 + 4 = 37

So the sequence is:
17, 21, 25, 29, 33, 37

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Pattern 2: Start at 73, subtract 9 each time

- 73 - 9 = 64
- 64 - 9 = 55
- 55 - 9 = 46
- 46 - 9 = 37
- 37 - 9 = 28

Sequence:
73, 64, 55, 46, 37, 28

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Pattern 3: Start at 26, add 12 each time

- 26 + 12 = 38
- 38 + 12 = 50
- 50 + 12 = 62
- 62 + 12 = 74
- 74 + 12 = 86

Sequence:
26, 38, 50, 62, 74, 86

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Pattern 4: Start at 95, subtract 17 each time

- 95 - 17 = 78
- 78 - 17 = 61
- 61 - 17 = 44
- 44 - 17 = 27
- 27 - 17 = 10

Sequence:
95, 78, 61, 44, 27, 10

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Part 2: Write the rule for each pattern and identify which number completes the sequence

Wait — looking again, it says “identify which number completes the sequence” but there are no multiple choices shown. Maybe it means just write the next number? Or perhaps it’s a typo and we’re just supposed to find the rule and continue the pattern? Since no options are given, I’ll assume we need to write the rule and then give the next number in the sequence (the one that would complete the blank).

Actually, re-reading: “Write the rule for each pattern, and identify which number completes the sequence.” But since there are blanks after each sequence, maybe “completes the sequence” means filling in the last blank? Let’s do that — find the rule, then compute the next number to fill the blank.

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Sequence A: 72, 66, 60, 54, ___, ___

Look at the differences:

- 72 → 66 = -6
- 66 → 60 = -6
- 60 → 54 = -6

Rule: Subtract 6

Next two numbers:

- 54 - 6 = 48
- 48 - 6 = 42

But the problem shows only one blank per line? Wait, looking back at the image description — actually, in the user’s text, each has two blanks? No — let me check:

In the original problem as typed:

> 72, 66, 60, 54, ___, ___
> Rule: ___

It shows two blanks. But then says “identify which number completes the sequence” — singular. Hmm. Maybe it’s a mistake, or perhaps they want the very next number? To be safe, I’ll provide the rule and the next number (first blank), since that’s what “completes” might mean — the immediate next term.

But let’s look at all sequences — they all have two blanks except possibly miswritten. Actually, in the user input:

“72, 66, 60, 54, ___, ___” — two blanks
“19, 32, 45, 58, ___, ___” — two blanks
etc.

And then “Rule: ___”

So probably, we are to write the rule and then fill both blanks? But the instruction says “identify which number completes the sequence” — singular. This is confusing.

Wait — perhaps “which number completes the sequence” refers to choosing from options not shown? But none are provided. Given the context, I think the safest interpretation is: for each sequence, determine the rule, and then write the next number (filling the first blank) as the one that “completes” the visible part. But since two blanks are shown, maybe we should fill both? However, the answer format likely expects just the rule and perhaps the next number.

Looking at standard worksheets like this, often they ask for the rule and then the next term. Also, the phrase “which number completes the sequence” suggests one number — so likely the next one after the last given.

I’ll go with: for each, state the rule and give the next number (first blank). If needed, I can note the second too, but for final answer, I’ll list rule and next number.

Alternatively, maybe “completes the sequence” means the last number in the full pattern shown? But without more context, I’ll proceed as follows:

For each sequence:

- Find the rule (how much added or subtracted each time)
- Apply it once to get the next number (to fill the first blank)

That seems most reasonable.

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Sequence A: 72, 66, 60, 54, ...

Difference: 66 - 72 = -6; 60 - 66 = -6; 54 - 60 = -6 → constant difference of -6

Rule: Subtract 6

Next number: 54 - 6 = 48

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Sequence B: 19, 32, 45, 58, ...

Differences:

32 - 19 = 13
45 - 32 = 13
58 - 45 = 13

Rule: Add 13

Next number: 58 + 13 = 71

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Sequence C: 37, 46, 55, 64, ...

Differences:

46 - 37 = 9
55 - 46 = 9
64 - 55 = 9

Rule: Add 9

Next number: 64 + 9 = 73

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Sequence D: 84, 71, 58, 45, ...

Differences:

71 - 84 = -13
58 - 71 = -13
45 - 58 = -13

Rule: Subtract 13

Next number: 45 - 13 = 32

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Now, compiling all answers.

Final Answer:

Part 1:

1. 17, 21, 25, 29, 33, 37
2. 73, 64, 55, 46, 37, 28
3. 26, 38, 50, 62, 74, 86
4. 95, 78, 61, 44, 27, 10

Part 2:

1. Rule: Subtract 6; Next number: 48
2. Rule: Add 13; Next number: 71
3. Rule: Add 9; Next number: 73
4. Rule: Subtract 13; Next number: 32

But wait — in Part 2, the problem says “identify which number completes the sequence”. Since there are two blanks, maybe they want both? But the wording is singular. Perhaps in the actual worksheet, there are multiple choice options for “which number”, but since none are provided here, I’ll stick with providing the rule and the next number.

To match typical expectations, I’ll present the answers clearly.

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Final Answer:
Part 1:
1. 21, 25, 29, 33, 37
2. 64, 55, 46, 37, 28
3. 38, 50, 62, 74, 86
4. 78, 61, 44, 27, 10

Part 2:
1. Rule: Subtract 6; Completing number: 48
2. Rule: Add 13; Completing number: 71
3. Rule: Add 9; Completing number: 73
4. Rule: Subtract 13; Completing number: 32