Math worksheet with numerical series to complete.

Let’s solve each numerical series one by one, looking for patterns — alternating operations, arithmetic sequences, geometric sequences, Fibonacci-like patterns, or combinations.

---

1) 4, 8, 10, 20, 22, 44, __, __, __

Pattern:
Look at the pattern:
- 4 × 2 = 8
- 8 + 2 = 10
- 10 × 2 = 20
- 20 + 2 = 22
- 22 × 2 = 44
→ So the pattern alternates: ×2, +2, ×2, +2, ...

Next:
- 44 + 2 = 46
- 46 × 2 = 92
- 92 + 2 = 94

✔ Answer: 46, 92, 94

---

2) 1, 3, -1, -3, -7, -21, __, __, __

Let’s look at differences or operations:

From 1 to 3: +2
3 to -1: -4
-1 to -3: -2
-3 to -7: -4
-7 to -21: ×3? Not consistent.

Wait — maybe split into two interleaved sequences?

Odd positions (1st, 3rd, 5th...): 1, -1, -7 → ?
Even positions (2nd, 4th, 6th...): 3, -3, -21 → ?

Check even positions: 3, -3, -21
3 → -3: ×(-1)
-3 → -21: ×7 → not clear.

Alternative: Look at recursive pattern:

Try:
Term 3 = Term 2 - 4 → 3 - 4 = -1
Term 4 = Term 3 - 2 → -1 - 2 = -3
Term 5 = Term 4 - 4 → -3 - 4 = -7
Term 6 = Term 5 × 3 → -7 × 3 = -21

Hmm — inconsistent.

Wait — another idea: Maybe multiply and subtract?

Let’s try:

From term 1 to 2: 1 × 3 = 3
Term 2 to 3: 3 - 4 = -1
Term 3 to 4: -1 × 3 = -3
Term 4 to 5: -3 - 4 = -7
Term 5 to 6: -7 × 3 = -21

Ah! Pattern: ×3, then -4, repeat

So:
Term 6 = -21
Term 7 = -21 - 4 = -25
Term 8 = -25 × 3 = -75
Term 9 = -75 - 4 = -79

✔ Answer: -25, -75, -79

---

3) 0, 1, 1, 2, 3, 5, 8, __, __, __

This is the Fibonacci sequence!

Each term = sum of previous two:
0, 1, 1 (0+1), 2 (1+1), 3 (1+2), 5 (2+3), 8 (3+5)

Next:
8 + 5 = 13
13 + 8 = 21
21 + 13 = 34

✔ Answer: 13, 21, 34

---

4) 4, 12, 16, 48, 52, 156, 160, __, __, __

Look at pattern:

4 → 12: ×3
12 → 16: +4
16 → 48: ×3
48 → 52: +4
52 → 156: ×3
156 → 160: +4
→ Pattern: ×3, +4, ×3, +4, ...

Next:
160 × 3 = 480
480 + 4 = 484
484 × 3 = 1452

✔ Answer: 480, 484, 1452

---

5) 9, 12, 7, 10, 5, 8, 3, __, __, __

Alternate between two sequences:

Odd positions: 9, 7, 5, 3 → decreasing by 2 → next: 1, -1

Even positions: 12, 10, 8 → decreasing by 2 → next: 6

But we need 3 more terms. The last given term is 3 (position 7). Next is position 8 (even), then 9 (odd), then 10 (even).

So:
Position 8 (even): 8 - 2 = 6
Position 9 (odd): 3 - 2 = 1
Position 10 (even): 6 - 2 = 4

✔ Answer: 6, 1, 4

---

6) 16, 22, 19, 25, 22, 28, 25, __, __, __

Again, split into two interleaved sequences:

Odd positions: 16, 19, 22, 25 → +3 each time → next: 28, 31

Even positions: 22, 25, 28 → +3 each time → next: 31

We have 7 terms given. Next three are positions 8, 9, 10.

Position 8 (even): 28 + 3 = 31
Position 9 (odd): 25 + 3 = 28
Position 10 (even): 31 + 3 = 34

✔ Answer: 31, 28, 34

---

7) 4, 12, 16, 48, 52, 156, 160, __, __, __

Wait — this is identical to problem 4!

Same numbers: 4, 12, 16, 48, 52, 156, 160,...

So same pattern: ×3, +4, ×3, +4...

As in #4:

160 × 3 = 480
480 + 4 = 484
484 × 3 = 1452

✔ Answer: 480, 484, 1452

---

8) 4, 8, 1, 2, -5, -10, -17, __, __, __

Look at differences:

8 - 4 = +4
1 - 8 = -7
2 - 1 = +1
-5 - 2 = -7
-10 - (-5) = -5
-17 - (-10) = -7

Not obvious.

Try grouping:

Group 1: 4, 8 → ×2
Group 2: 1, 2 → ×2
Group 3: -5, -10 → ×2
Group 4: -17, ? → should be ×2 → -34

Then next? After ×2, maybe subtract something?

After 8 → 1: 8 - 7 = 1
After 2 → -5: 2 - 7 = -5
After -10 → -17: -10 - 7 = -17
→ So after each pair, subtract 7 to get next starting number.

So:
-17 × 2 = -34
Then -34 - 7 = -41
Then -41 × 2 = -82

✔ Answer: -34, -41, -82

---

9) 22, 28, 21, 27, 20, 26, 19, __, __, __

Split into two sequences:

Odd positions: 22, 21, 20, 19 → decreasing by 1 → next: 18, 17

Even positions: 28, 27, 26 → decreasing by 1 → next: 25

Positions:
Given up to 7th term (19). Next three: 8th (even), 9th (odd), 10th (even)

8th: 26 - 1 = 25
9th: 19 - 1 = 18
10th: 25 - 1 = 24

✔ Answer: 25, 18, 24

---

10) 1, 2, -4, -8, -14, -28, -34, __, __, __

Look at pattern:

1 → 2: ×2
2 → -4: -6? Or ×(-2)?
-4 → -8: ×2
-8 → -14: -6
-14 → -28: ×2
-28 → -34: -6

Pattern: ×2, then -6, repeat

So:
-34 × 2 = -68
-68 - 6 = -74
-74 × 2 = -148

✔ Answer: -68, -74, -148

---

## ✔ Final Answers:

1) 46, 92, 94
2) -25, -75, -79
3) 13, 21, 34
4) 480, 484, 1452
5) 6, 1, 4
6) 31, 28, 34
7) 480, 484, 1452
8) -34, -41, -82
9) 25, 18, 24
10) -68, -74, -148

Let me know if you’d like a visual chart or explanation for any specific one!