Patterns Worksheets- Complete the Numerical Series Worksheets ... - Free Printable

Let's solve each numerical series step by step and explain the pattern.

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1) 25, 26, 22, 23, 19, 20, 16, __, __, __

Step-by-step analysis:
- Look at positions:
- Odd positions (1st, 3rd, 5th, 7th): 25, 22, 19, 16 → decreasing by 3
- 25 → 22 → 19 → 16 → next: 13
- Even positions (2nd, 4th, 6th, 8th): 26, 23, 20, ? → also decreasing by 3
- 26 → 23 → 20 → next: 17
- Then odd position after that: 13 → next even: 17 → then odd: 13 → next even: 14? Wait — let’s list:

Positions:
1. 25
2. 26
3. 22
4. 23
5. 19
6. 20
7. 16
8. ? → should be 17 (since 26, 23, 20, 17)
9. ? → odd: 13 (16 - 3)
10. ? → even: 14 (17 - 3)

Wait — but 17 → 14? No, we already had 20 → next is 17, so 17 → 14?

But wait:
Even numbers: 26, 23, 20, 17 → yes, -3 each time
Odd numbers: 25, 22, 19, 16, 13 → -3 each

So:
- 8th term: 17
- 9th term: 13
- 10th term: 14

But the series ends at 16 (7th), so missing are 8th, 9th, 10th.

So:
- 8th = 17
- 9th = 13
- 10th = 14

✔ Answer: 17, 13, 14

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2) 1, 4, 3, 6, 5, 8, 7, __, __, __

Look at pattern:
- 1, 4, 3, 6, 5, 8, 7, ?

Group into pairs or look at alternating sequences.

Odd positions: 1st, 3rd, 5th, 7th → 1, 3, 5, 7 → increasing by 2 → next: 9
Even positions: 2nd, 4th, 6th, 8th → 4, 6, 8, ? → increasing by 2 → next: 10

So:
- 8th = 10
- 9th = 11 (odd sequence: 1,3,5,7,9,11)
- 10th = 12 (even: 4,6,8,10,12)

But we only need 3 blanks: after 7 → so 8th, 9th, 10th.

So:
- 8th = 10
- 9th = 9
- 10th = 12

Wait: 7th is 7 → 8th is even → 10
Then 9th is odd → 9
Then 10th is even → 12

So: 10, 9, 12

But let's verify:

Sequence:
1 (odd), 4 (even), 3 (odd), 6 (even), 5 (odd), 8 (even), 7 (odd), 10 (even), 9 (odd), 12 (even)

Yes, alternating between two sequences:
- Odd positions: 1,3,5,7,9,... → +2
- Even positions: 4,6,8,10,12,... → +2

✔ Answer: 10, 9, 12

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3) 17, 21, 14, 18, 11, 15, 8, __, __, __

Break it down:

Look at positions:
- 1st: 17
- 2nd: 21
- 3rd: 14
- 4th: 18
- 5th: 11
- 6th: 15
- 7th: 8
- 8th: ?
- 9th: ?
- 10th: ?

Try grouping:

Odd positions: 1st, 3rd, 5th, 7th → 17, 14, 11, 8 → decreasing by 3 → next: 5
Even positions: 2nd, 4th, 6th, 8th → 21, 18, 15, ? → decreasing by 3 → next: 12

So:
- 8th = 12
- 9th = 5 (next odd)
- 10th = ? → even → next even: 12 → 9 → 12 → 15 → 12 → next even: 9? Wait no:

Even positions: 21, 18, 15, 12 → so 10th is next even → 12 → 9? No:

Wait: even terms: 21 (2nd), 18 (4th), 15 (6th), 12 (8th), then 10th would be next even → 9? No, pattern is -3 each time.

So:
- 8th = 12
- 9th = 5
- 10th = 9? No — 10th is even → 12 → 9? No.

Wait: even positions:
- 2nd: 21
- 4th: 18
- 6th: 15
- 8th: 12
- 10th: 9 → since 12 - 3 = 9

Yes.

So:
- 8th = 12
- 9th = 5
- 10th = 9

✔ Answer: 12, 5, 9

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4) 23, 26, 19, 22, 15, 18, 11, __, __, __

Check pattern:

Odd positions: 1st, 3rd, 5th, 7th → 23, 19, 15, 11 → decreasing by 4 → next: 7
Even positions: 2nd, 4th, 6th, 8th → 26, 22, 18, ? → decreasing by 4 → next: 14

So:
- 8th = 14
- 9th = 7
- 10th = 10? Wait: even after 14 → next even: 10?

No: even positions: 26, 22, 18, 14 → next even (10th): 10? But 14 - 4 = 10

Yes.

So:
- 8th = 14
- 9th = 7
- 10th = 10

✔ Answer: 14, 7, 10

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5) 24, 30, 26, 32, 28, 34, 30, __, __, __

Look at odd and even positions:

Odd: 1st, 3rd, 5th, 7th → 24, 26, 28, 30 → increasing by 2 → next: 32
Even: 2nd, 4th, 6th, 8th → 30, 32, 34, ? → increasing by 2 → next: 36

So:
- 8th = 36
- 9th = 32
- 10th = 38

Wait: after 30 (7th), 8th is even → 36
9th is odd → 32
10th is even → 38

Yes.

✔ Answer: 36, 32, 38

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6) 3, 4, 0, 1, -3, -2, -6, __, __, __

Look at positions:

Odd: 1st, 3rd, 5th, 7th → 3, 0, -3, -6 → decreasing by 3 → next: -9
Even: 2nd, 4th, 6th, 8th → 4, 1, -2, ? → decreasing by 3 → next: -5

So:
- 8th = -5
- 9th = -9
- 10th = -8 (next even: -5 → -8? No: even sequence: 4,1,-2,-5 → -8?)

Wait: 4 → 1 → -2 → -5 → next: -8? Yes, -5 - 3 = -8

So:
- 8th = -5
- 9th = -9
- 10th = -8

✔ Answer: -5, -9, -8

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7) 25, 27, 22, 24, 19, 21, 16, __, __, __

Odd positions: 1st, 3rd, 5th, 7th → 25, 22, 19, 16 → decreasing by 3 → next: 13
Even positions: 2nd, 4th, 6th, 8th → 27, 24, 21, ? → decreasing by 3 → next: 18

So:
- 8th = 18
- 9th = 13
- 10th = 15? Wait: even after 18 → next even: 15? No.

Even positions: 27, 24, 21, 18 → next even (10th): 15? No, 18 - 3 = 15

Yes.

So:
- 8th = 18
- 9th = 13
- 10th = 15

✔ Answer: 18, 13, 15

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8) 7, 14, 13, 20, 19, 26, 25, __, __, __

Look at pattern:

Group as pairs or alternate:

Odd positions: 1st, 3rd, 5th, 7th → 7, 13, 19, 25 → increasing by 6 → next: 31
Even positions: 2nd, 4th, 6th, 8th → 14, 20, 26, ? → increasing by 6 → next: 32

So:
- 8th = 32
- 9th = 31
- 10th = 38? Wait: even after 32 → 32 + 6 = 38?

No: even positions: 14, 20, 26, 32 → next even (10th): 38

Yes.

So:
- 8th = 32
- 9th = 31
- 10th = 38

✔ Answer: 32, 31, 38

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9) 0, 1, 1, 2, 3, 5, 8, __, __, __

This is the Fibonacci sequence!

Each number is sum of previous two:

- 0, 1
- 1 = 0+1
- 2 = 1+1
- 3 = 1+2
- 5 = 2+3
- 8 = 3+5
- Next: 5+8 = 13
- Then: 8+13 = 21
- Then: 13+21 = 34

✔ Answer: 13, 21, 34

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10) 22, 28, 27, 33, 32, 38, 37, __, __, __

Look at pattern:

Group in pairs:

- 22, 28 → +6
- 27, 33 → +6
- 32, 38 → +6
- 37, ? → +6 → 43?

But check the structure:

List:
1. 22
2. 28 (+6)
3. 27 (-1)
4. 33 (+6)
5. 32 (-1)
6. 38 (+6)
7. 37 (-1)
8. ? → +6 → 43?
9. ? → -1 → 42?
10. ? → +6 → 48?

Pattern: +6, -1, +6, -1, +6, -1, +6, -1, +6...

So:
- After 37 (7th), 8th = 37 + 6 = 43
- 9th = 43 - 1 = 42
- 10th = 42 + 6 = 48

✔ Answer: 43, 42, 48

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## ✔ Final Answers:

1) 17, 13, 14
2) 10, 9, 12
3) 12, 5, 9
4) 14, 7, 10
5) 36, 32, 38
6) -5, -9, -8
7) 18, 13, 15
8) 32, 31, 38
9) 13, 21, 34
10) 43, 42, 48

Let me know if you'd like these explained in a table or formatted for printing!