Let's solve each sequence step by step.
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1. Sequence: 5, 9, 13, 17, ……
(a) Write down the next term in this sequence.
Let’s look at the pattern:
- 9 - 5 = 4
- 13 - 9 = 4
- 17 - 13 = 4
Each term increases by
4.
So, the next term is:
> 17 + 4 =
21
✔ Answer (a): 21
(b) Describe the rule for continuing the sequence.
The rule is:
Add 4 to the previous term.
Or more formally: This is an
arithmetic sequence with a common difference of 4.
✔ Answer (b): Add 4 to the previous term.
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2. Sequence: 2, 6, 18, 54, ……
(a) Write down the next term in this sequence.
Check the pattern:
- 6 ÷ 2 = 3
- 18 ÷ 6 = 3
- 54 ÷ 18 = 3
Each term is multiplied by
3.
So, next term:
> 54 × 3 =
162
✔ Answer (a): 162
(b) Describe the rule for continuing the sequence.
The rule is:
Multiply the previous term by 3.
This is a
geometric sequence with a common ratio of 3.
✔ Answer (b): Multiply the previous term by 3.
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3. Sequence: 256, 128, 64, 32, ……
(a) Write down the next term in this sequence.
Look at the pattern:
- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
Each term is divided by
2 (or multiplied by 0.5).
So, next term:
> 32 ÷ 2 =
16
✔ Answer (a): 16
(b) Describe the rule for continuing the sequence.
The rule is:
Divide the previous term by 2.
Alternatively:
Multiply the previous term by ½.
This is a geometric sequence with a common ratio of ½.
✔ Answer (b): Divide the previous term by 2.
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✔ Final Answers:
####
1.
(a)
21
(b)
Add 4 to the previous term.
####
2.
(a)
162
(b)
Multiply the previous term by 3.
####
3.
(a)
16
(b)
Divide the previous term by 2.
Let me know if you'd like these written in a formatted worksheet style!
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet year 7.
