Number patterns worksheet for students to identify and complete sequences.

Let’s solve each number pattern step by step.

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Problem 1:
Numbers: 2, 4, 6, 8, 10, 12, 14, 18
Wait — let’s check the pattern. From 2 to 4 is +2, 4 to 6 is +2, 6 to 8 is +2… all the way to 14. But then 14 to 18 is +4? That breaks the pattern. Let me double-check the image.

Actually, looking again — the last box says 18, but if we’re counting by 2s from 2, after 14 should be 16, then 18. So maybe there’s a missing box? The sequence shown has 8 boxes: positions 1 to 8.

Let’s list them with position:

1: 2
2: 4
3: 6
4: 8
5: 10
6: 12
7: 14
8: 18 ← this should be 16 if it’s +2 each time.

But wait — maybe it’s a typo in the problem? Or perhaps I misread. Let me count the steps between numbers:

From 2 to 4 → +2
4 to 6 → +2
6 to 8 → +2
8 to 10 → +2
10 to 12 → +2
12 to 14 → +2
14 to 18 → +4 ✘

That doesn’t fit. Unless... maybe the last number is meant to be 16? But the image clearly shows 18.

Hold on — let’s look at how many numbers are listed: 8 numbers total.

If we start at 2 and add 2 each time:

Term 1: 2
Term 2: 4
Term 3: 6
Term 4: 8
Term 5: 10
Term 6: 12
Term 7: 14
Term 8: 16 ← but image says 18.

This is inconsistent. Maybe it’s not starting from 2? Or maybe it’s counting by 2s but skipping one? No, that doesn’t make sense for a basic pattern worksheet.

Wait — perhaps I made a mistake in reading the image. Let me re-express the sequence as given:

Box 1: 2
Box 2: 4
Box 3: 6
Box 4: 8
Box 5: 10
Box 6: 12
Box 7: 14
Box 8: 18

The jump from 14 to 18 is +4, which breaks the +2 pattern. But all previous jumps are +2. This must be an error — either in the image or in my reading.

Alternatively, maybe the pattern is “counting even numbers” and they skipped 16 by accident? But for a student worksheet, that would be confusing.

Let me check the other problems to see if there’s a consistent style.

Problem 2: 4, 8, 12, 16, 20, 24, 28, 32 → clearly +4 each time. Good.

Problem 3: 5, 10, 15, 20, 25, 30, 35, 40 → +5 each time. Good.

Problem 4: 10, 20, 30, 40, 50, 60, 70, 80 → +10 each time. Good.

So Problem 1 should also be consistent. Likely, the last number is supposed to be 16, not 18. Because 2,4,6,8,10,12,14,16 is perfect +2.

Perhaps it’s a printing error in the image. Since this is a standard elementary math worksheet, and all others follow clean patterns, I’ll assume Problem 1 is meant to be 2,4,6,8,10,12,14,16 — so the last box should be 16, not 18.

But the user provided the image as-is. Should I go with what’s written?

Wait — let’s count the boxes again. In the image description, it says:

“1. [2] [4] [6] [8] [10] [12] [14] [18]”

That’s 8 boxes. If it’s counting by 2s starting from 2, the 8th term should be 2 + (8-1)*2 = 2 + 14 = 16.

So 18 is incorrect. But since this is a homework help task, and the student is expected to recognize the pattern, I think the intended answer is that we are counting by 2s, starting from 2 to 16 — and the 18 is a typo.

Alternatively, maybe the pattern is different? Let’s see differences:

4-2=2
6-4=2
8-6=2
10-8=2
12-10=2
14-12=2
18-14=4 → only last difference is different.

That suggests it’s likely a mistake. For educational purposes, I will proceed assuming the pattern is +2 throughout, and the last number should be 16. Perhaps the student can note that, but for filling blanks, we go with the obvious pattern.

So for Problem 1:
We are counting even numbers; by 2's; starting from 2 to 16.

But the image says 18. Hmm.

Another possibility: maybe it’s counting by 2s but the last box is misprinted. I think for accuracy, I should point out the inconsistency, but since the instruction is to solve the problem accurately, and based on standard curriculum, I’ll go with the pattern being +2, so end at 16.

Wait — let’s calculate what the 8th term should be if starting at 2 and adding 2 seven times: 2 + 2*7 = 16. Yes.

So I’ll use 16 as the end, noting that the image may have a typo.

But to be faithful to the input, perhaps I should use 18? Then the pattern isn't consistent.

Let me think differently. Maybe the pattern is "multiples of 2" and they listed up to 18, but skipped 16? That would be odd.

No, I think it's safer to assume it's a typo and correct it to 16 for the sake of the pattern.

Proceeding with that assumption.

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Problem 1 (corrected):
Sequence: 2, 4, 6, 8, 10, 12, 14, 16
Pattern: Each number increases by 2.
So: We are counting even numbers; by 2's; starting from 2 to 16.

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Problem 2:
Sequence: 4, 8, 12, 16, 20, 24, 28, 32
Check differences:
8-4=4
12-8=4
16-12=4
20-16=4
24-20=4
28-24=4
32-28=4 → all +4. Perfect.

So: We are counting multiples of 4; by 4's; starting from 4 to 32.

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Problem 3:
Sequence: 5, 10, 15, 20, 25, 30, 35, 40
Differences: all +5.
So: We are counting multiples of 5; by 5's; starting from 5 to 40.

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Problem 4:
Sequence: 10, 20, 30, 40, 50, 60, 70, 80
Differences: all +10.
So: We are counting multiples of 10; by 10's; starting from 10 to 80.

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Now, for Problem 1, since the image shows 18, but logically it should be 16, I need to decide. Given that this is for a student, and the pattern is clear until the last number, I think the best approach is to fill in based on the pattern, and perhaps the student can ask the teacher about the discrepancy. But for the answer, I'll use 16 as the end, because 18 breaks the pattern.

Alternatively, if I must use 18, then the pattern isn't uniform, which is unlikely for this level.

I recall that in some worksheets, they might have a trick, but here all others are straightforward. So I'll go with 16.

Final decision: For Problem 1, end at 16.

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Final Answers:

1. We are counting even numbers; by 2's; starting from 2 to 16.
*(Note: Image shows 18, but pattern suggests 16)*

But since the instruction is to solve accurately, and to avoid confusion, perhaps I should state the pattern as observed.

Let me recalculate with 18 included.

If the sequence is 2,4,6,8,10,12,14,18, then the common difference is not constant. The first six intervals are +2, last is +4. That doesn't form a single arithmetic sequence.

Therefore, it must be an error. I will proceed with the corrected version.

For the purpose of this response, I'll provide answers based on the clear pattern, assuming typo in Problem 1.

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Final Answer:

1. We are counting even numbers; by 2's; starting from 2 to 16.
2. We are counting multiples of 4; by 4's; starting from 4 to 32.
3. We are counting multiples of 5; by 5's; starting from 5 to 40.
4. We are counting multiples of 10; by 10's; starting from 10 to 80.

But to match the image exactly for Problem 1, if I must use 18, then it's inconsistent. However, since the student is to complete the pattern, and the pattern is +2, the last number should be 16. I think it's reasonable to correct it.

Perhaps the image has 9 boxes? Let me count the boxes described:

In the user's message: "1. [2] [4] [6] [8] [10] [12] [14] [18]" — that's 8 boxes.

Standard for such worksheets is 8 terms. Term 8 should be 16.

I think it's safe to go with 16.

So final answers as above.