11+ Number Sequences (Year 6) | CGP Plus - Free Printable

Let's solve each of the number sequences step by step using the patterns and rules we can identify. We are given a box of possible numbers to choose from:

Available numbers:
81, 48, 2, 23, 71, 128

We need to find the next number in each sequence and pick it from this list.

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Sequence 1:

83, 71, 59, 47, 35, ______

Let’s look at the differences between consecutive terms:

- 83 → 71: -12
- 71 → 59: -12
- 59 → 47: -12
- 47 → 35: -12

So, the pattern is subtracting 12 each time.

Next term:
35 - 12 = 23

✔ Answer: 23

(23 is in the box)

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Sequence 2:

3, 6, 9, 11, 27, 16, ______

This one looks tricky because the pattern isn't consistent. Let's check the differences:

- 3 → 6: +3
- 6 → 9: +3
- 9 → 11: +2
- 11 → 27: +16
- 27 → 16: -11

No clear arithmetic pattern. Maybe two interleaved sequences?

Let’s split into odd positions (1st, 3rd, 5th, 7th) and even positions (2nd, 4th, 6th, 8th):

#### Odd positions:
- 1st: 3
- 3rd: 9
- 5th: 27
- 7th: ?

Pattern: 3 → 9 → 27 → ?
3 × 3 = 9
9 × 3 = 27
So next: 27 × 3 = 81

So the 7th term should be 81

Now check even positions:
- 2nd: 6
- 4th: 11
- 6th: 16

Differences:
- 6 → 11: +5
- 11 → 16: +5

So next even term would be +5 → 21, but that’s not in our box.

But we only need the next number, which is the 7th term — so 81

✔ Answer: 81

(81 is in the box)

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Sequence 3:

4, 8, 16, 32, 64, ______

Look at the pattern:

- 4 → 8: ×2
- 8 → 16: ×2
- 16 → 32: ×2
- 32 → 64: ×2

So it's doubling each time.

Next: 64 × 2 = 128

✔ Answer: 128

(128 is in the box)

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Sequence 4:

36, 43, 50, 57, 64, ______

Check differences:

- 36 → 43: +7
- 43 → 50: +7
- 50 → 57: +7
- 57 → 64: +7

So adding 7 each time.

Next: 64 + 7 = 71

✔ Answer: 71

(71 is in the box)

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Sequence 5:

58, 54, 51, 49, 48, ______

Look at differences:

- 58 → 54: -4
- 54 → 51: -3
- 51 → 49: -2
- 49 → 48: -1

So the amount subtracted is decreasing by 1 each time: -4, -3, -2, -1

Next: subtract 0 → 48 - 0 = 48

Wait — but that would be the same as previous? But let's see:

The pattern of subtraction:
-4, -3, -2, -1, then probably -0 → no change.

So next term: 48

But 48 is in the box!

But wait — is there a mistake? Let’s double-check:

- 58 → 54: -4
- 54 → 51: -3
- 51 → 49: -2
- 49 → 48: -1
- 48 → ? : -0 → 48

Yes, so next is 48

✔ Answer: 48

(48 is in the box)

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Sequence 6:

54, 9, 18, 18, 6, 27, ______

This seems complex. Let's look for a pattern.

List the terms:

1. 54
2. 9
3. 18
4. 18
5. 6
6. 27
7. ?

Try looking at alternating sequences.

#### Odd positions (1st, 3rd, 5th, 7th):
- 1st: 54
- 3rd: 18
- 5th: 6
- 7th: ?

Look at pattern:
54 → 18: ÷3
18 → 6: ÷3
So next: 6 ÷ 3 = 2

So 7th term = 2

#### Even positions (2nd, 4th, 6th):
- 2nd: 9
- 4th: 18
- 6th: 27

Pattern:
9 → 18: +9
18 → 27: +9
So next would be +9 → 36, but not needed.

We only need the 7th term → 2

✔ Answer: 2

(2 is in the box)

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✔ Final Answers:

1. 23
2. 81
3. 128
4. 71
5. 48
6. 2

All answers come from the given box: [81, 48, 2, 23, 71, 128]

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Summary Table:

| Sequence | Pattern | Next Number |
|--------|--------|-------------|
| 1. 83, 71, 59, 47, 35 | Subtract 12 | 23 |
| 2. 3, 6, 9, 11, 27, 16 | Alternating: odd positions ×3 | 81 |
| 3. 4, 8, 16, 32, 64 | Multiply by 2 | 128 |
| 4. 36, 43, 50, 57, 64 | Add 7 | 71 |
| 5. 58, 54, 51, 49, 48 | Subtract decreasing values (-4,-3,-2,-1,0) | 48 |
| 6. 54, 9, 18, 18, 6, 27 | Alternating: odd positions ÷3 | 2 |

✔ All solved!