Worksheet for identifying and continuing repeating patterns using shapes, arrows, letters, and numbers.

Let's solve each pattern step by step and explain the reasoning behind each.

---

a. □ ○ ○ □ ○ ○ □ ○ ○ □ ___ ___ ___

Pattern:
Look at the sequence:
□ ○ ○ □ ○ ○ □ ○ ○ □

We can break it into groups:
(□ ○ ○) (□ ○ ○) (□ ○ ○) (□)

So, the repeating unit is □ ○ ○, which repeats every 3 shapes.

- After the last □, we expect the next two to be ○ ○.
- Then the pattern would repeat again with □.

But since there are only three blanks, let’s count:

After the last □ (the 10th shape), the pattern continues:
- 11th: ○
- 12th: ○
- 13th: □

✔ So, fill in: ○ ○ □

---

b. ↑↓↑↓↑↓↑↓↑↓↑↓___ ___ ___

This one is alternating arrows:
↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓

Clearly, the pattern is ↑ ↓, repeating every 2 shapes.

Last shape is ↓ (12th shape). So:

- 13th: ↑
- 14th: ↓
- 15th: ↑

✔ Fill in: ↑ ↓ ↑

---

c. A B A C A D A E A F A ___ ___ ___

Let’s look closely:

A B A C A D A E A F A

Break it down:

- A B
- A C
- A D
- A E
- A F
- A ?

Notice that after each "A", a new letter appears: B, C, D, E, F...

So the pattern is:
A + next letter in alphabet → then back to A

Sequence of letters after A:
B, C, D, E, F → next should be G

Then again: A G

So after the last A (the 11th letter), we expect:

- 12th: G
- 13th: A
- 14th: H? Wait — let’s double-check.

Wait — the full sequence is:

1. A
2. B
3. A
4. C
5. A
6. D
7. A
8. E
9. A
10. F
11. A

So positions:
Odd positions (1,3,5,7,9,11): all A
Even positions (2,4,6,8,10): B, C, D, E, F → increasing alphabet

So:
- 12th (even): should be G
- 13th (odd): A
- 14th (even): H

But we have only 3 blanks after the 11th shape.

So:
- 12th: G
- 13th: A
- 14th: H

✔ Fill in: G A H

---

d. ◆◇◆◇◆◇◆◇◆◇◆◇___ ___ ___

Pattern:
◆ ◇ ◆ ◇ ◆ ◇ ◆ ◇ ◆ ◇ ◆ ◇

Repeating pair: ◆ ◇

It alternates every shape.

Last shape is ◇ (12th shape)

So:
- 13th: ◆
- 14th: ◇
- 15th: ◆

✔ Fill in: ◆ ◇ ◆

---

e. 1 2 3 8 2 1 1 2 3 8 2 1 1 2 3 8 2 1 ___ ___ ___

This one looks more complex.

List the numbers:

Position:
1: 1
2: 2
3: 3
4: 8
5: 2
6: 1
7: 1
8: 2
9: 3
10: 8
11: 2
12: 1
13: 1
14: 2
15: 3
16: 8
17: 2
18: 1
19: ?
20: ?
21: ?

Now look for repeating patterns.

Group them:

From position 1–6: 1 2 3 8 2 1
Then 7–12: 1 2 3 8 2 1
Then 13–18: 1 2 3 8 2 1

Wait! Let’s check:

- 1–6: 1 2 3 8 2 1
- 7–12: 1 2 3 8 2 1
- 13–18: 1 2 3 8 2 1

Yes! It's repeating 1 2 3 8 2 1 every 6 numbers.

So the cycle is: 1 2 3 8 2 1 (length 6)

Now check:

- 19th: start of next cycle → 1
- 20th: 2
- 21st: 3

✔ Fill in: 1 2 3

---

✔ Final Answers:

a. ○ ○ □
b. ↑ ↓ ↑
c. G A H
d. ◆ ◇ ◆
e. 1 2 3

---

Summary of Patterns:

| Problem | Pattern | Next 3 |
|--------|--------|--------|
| a | □ ○ ○ repeats | ○ ○ □ |
| b | ↑ ↓ repeats | ↑ ↓ ↑ |
| c | A followed by increasing letter (B,C,D,...) | G A H |
| d | ◆ ◇ repeats | ◆ ◇ ◆ |
| e | 1 2 3 8 2 1 repeats | 1 2 3 |

You can now fill in the blanks on the worksheet accordingly.