Third Grade Patterns Worksheets - Free Printable

Let’s go through each pattern one by one and find the rule, then fill in the missing numbers.

---

**Pattern 1:
1, 4, 7, 10, 13, 16, 19, 22, 25, ___, ___, ___**

Look at how much we add each time:

4 - 1 = 3
7 - 4 = 3
10 - 7 = 3 → so it’s adding 3 each time.

So after 25:
25 + 3 = 28
28 + 3 = 31
31 + 3 = 34

✔ Pattern: Add 3

---

**Pattern 2:
3, 8, 13, 18, 23, 33, 38, ___, ___, ___**

Wait — let’s check the differences:

8 - 3 = 5
13 - 8 = 5
18 - 13 = 5
23 - 18 = 5
Then… 33? That’s a jump of 10! Hmm, maybe that’s a typo? Let’s see next:
38 - 33 = 5 → so probably “33” should be “28”? But since it’s written as 33, let’s assume it’s correct for now.

Actually, looking again:
After 23, if we add 5, we get 28 — but it says 33. Then 38 is +5 from 33. So maybe there’s a mistake in the problem? Or perhaps it’s two patterns?

Wait — let’s list them with positions:

Position 1: 3
Position 2: 8 (+5)
Position 3: 13 (+5)
Position 4: 18 (+5)
Position 5: 23 (+5)
Position 6: 33 → that’s +10? That breaks the pattern.
Position 7: 38 → +5 again.

This seems inconsistent. Maybe it’s supposed to be 28 instead of 33? Because otherwise the pattern doesn’t hold.

But since this is a student worksheet, likely it’s a typo, and it should be 28. Let’s assume that for consistency.

So corrected:
3, 8, 13, 18, 23, 28, 33, 38 → wait no, original has 33 then 38.

Alternative idea: Maybe it’s alternating? No.

Another possibility: Perhaps “33” is a misprint and should be “28”. Since 23 + 5 = 28, then 28 + 5 = 33, then 33 + 5 = 38 — that makes sense!

Ah! So the sequence is:
3, 8, 13, 18, 23, 28, 33, 38 — but the worksheet wrote “33” where “28” should be? Wait no — look:

Original:
3, 8, 13, 18, 23, 33, 38 → that skips 28.

That must be an error. For the sake of solving, I’ll assume it’s meant to be increasing by 5 each time.

So after 38:
38 + 5 = 43
43 + 5 = 48
48 + 5 = 53

And the pattern is: Add 5

But to match the given numbers, even though 33 appears after 23 (which is +10), maybe it’s intentional? Let’s double-check.

If we force it:
From 23 to 33 is +10, then 33 to 38 is +5 — that’s not consistent.

I think it’s safe to assume it’s a typo and should be 28. Many worksheets have such errors. We’ll proceed with +5 throughout.

✔ Pattern: Add 5 → so missing: 43, 48, 53

---

**Pattern 3:
8, 15, 17, 24, 26, 33, 35, ___, ___, ___**

Let’s look at differences:

15 - 8 = 7
17 - 15 = 2
24 - 17 = 7
26 - 24 = 2
33 - 26 = 7
35 - 33 = 2

So the pattern alternates: +7, +2, +7, +2, ...

So after 35:
+7 → 35 + 7 = 42
+2 → 42 + 2 = 44
+7 → 44 + 7 = 51

✔ Pattern: Alternate adding 7 and 2

---

**Pattern 4:
25, 23, 21, 19, 17, 15, ___, ___, ___, ___, ___**

Each time subtract 2:

25 - 2 = 23
23 - 2 = 21
...
15 - 2 = 13
13 - 2 = 11
11 - 2 = 9
9 - 2 = 7
7 - 2 = 5

✔ Pattern: Subtract 2

---

**Pattern 5:
3, 6, 12, 24, ___, 96, 192, ___, ___, ___**

Check ratios:

6 ÷ 3 = 2
12 ÷ 6 = 2
24 ÷ 12 = 2 → so multiply by 2 each time.

After 24:
24 × 2 = 48
Then 48 × 2 = 96 ✓ matches
96 × 2 = 192 ✓ matches
Then:
192 × 2 = 384
384 × 2 = 768
768 × 2 = 1536

✔ Pattern: Multiply by 2

---

**Bonus: Secret Pattern
0, 1, 4, 9, 16, 25, 36, 49, 64, 81**

These are perfect squares!

0 = 0²
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
36 = 6²
49 = 7²
64 = 8²
81 = 9²

So the secret pattern is: Square numbers (n² starting from n=0)

The question asks: “What is the secret pattern?” — so answer is: These are square numbers.

---

Now, compiling all answers:

Final Answer:

1. 28, 31, 34
2. 43, 48, 53 *(assuming typo in original; should be +5 throughout)*
3. 42, 44, 51
4. 13, 11, 9, 7, 5
5. 48, 384, 768, 1536
Bonus: Square numbers (or n² for n = 0,1,2,...)