Let’s solve the “Now Try These” section step by step.
We are given 5 sequences, and we must choose the correct next number from this box:
>
81 48 2 23 71 128
---
Sequence 1:
83 71 59 47 35 ________
Look at the differences between consecutive numbers:
- 83 → 71 =
–12
- 71 → 59 =
–12
- 59 → 47 =
–12
- 47 → 35 =
–12
✔ Pattern: Subtract 12 each time.
So, next number:
35 – 12 = 23
✔️
Answer: 23 (in the box)
---
Sequence 2:
3 6 9 11 27 16 ________
This looks messy. Let’s try splitting into
alternating positions (like the example with 88, 8, 4, 16, 22, 32, 11).
Split into two sequences:
-
Odd positions (1st, 3rd, 5th, 7th): 3, 9, 27, ?
-
Even positions (2nd, 4th, 6th): 6, 11, 16
#### Even positions: 6, 11, 16
- 6 → 11 = +5
- 11 → 16 = +5
Pattern: Add 5 → next would be 21, but we don’t need it — we’re looking for the 7th term, which is odd position.
#### Odd positions: 3, 9, 27, ?
- 3 × 3 = 9
- 9 × 3 = 27
- 27 × 3 =
81
✔ Pattern: Multiply by 3.
✔️
Answer: 81 (in the box)
---
Sequence 3:
4 8 16 32 64 ________
This is straightforward:
- 4 × 2 = 8
- 8 × 2 = 16
- 16 × 2 = 32
- 32 × 2 = 64
- 64 × 2 =
128
✔ Pattern: Doubling each time.
✔️
Answer: 128 (in the box)
---
Sequence 4:
36 43 50 57 64 ________
Check differences:
- 36 → 43 = +7
- 43 → 50 = +7
- 50 → 57 = +7
- 57 → 64 = +7
✔ Pattern: Add 7.
Next:
64 + 7 = 71
✔️
Answer: 71 (in the box)
---
Sequence 5:
58 54 51 49 48 ________
Look at the differences:
- 58 → 54 =
–4
- 54 → 51 =
–3
- 51 → 49 =
–2
- 49 → 48 =
–1
Pattern: Subtract decreasing numbers: –4, –3, –2, –1
Next should be:
–0? That doesn’t make sense.
Wait — maybe the pattern is subtracting 4, then 3, then 2, then 1 — so next is subtract
0? But that would mean 48 again.
But let’s check if it’s continuing to decrease by smaller amounts:
Actually, after –1, the next subtraction might be
–0, meaning no change → 48.
But 48 is already in the sequence. And 48 is in the box — but let’s see if there’s another way.
Alternatively, maybe it’s a pattern of subtracting 4, then 3, then 2, then 1 — so next is subtract 0 → still 48.
But perhaps it’s a trick — maybe it’s going down to 48 and stopping? But we need to pick from the box.
Wait — look at the box:
81, 48, 2, 23, 71, 128
We’ve already used 23, 81, 128, 71.
Left:
48 and
2
If the pattern is: subtract 4, 3, 2, 1 → next subtract 0 → stays 48.
That’s plausible.
But let’s double-check — is there another pattern?
What if we look at the differences of differences?
Sequence: 58, 54, 51, 49, 48
First differences: –4, –3, –2, –1
Second differences: +1, +1, +1 → constant second difference? No, first differences are linearly increasing by +1.
So next first difference should be
0 → next term = 48 + 0 = 48.
✔ So answer is
48
✔️
Answer: 48 (in the box)
---
## Final Answers:
1.
23
2.
81
3.
128
4.
71
5.
48
All chosen from the box:
✔ 81, 48, 2, 23, 71, 128 — we used all except
2, which is fine — not every number needs to be used.
---
## Summary:
| Sequence | Pattern | Next Number |
|----------|-----------------------------|-------------|
| 1 | Subtract 12 | 23 |
| 2 | Alternating: ×3 (odd pos) | 81 |
| 3 | Multiply by 2 | 128 |
| 4 | Add 7 | 71 |
| 5 | Subtract 4,3,2,1 → then 0 | 48 |
✔ All answers are in the provided box.
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 6.
