NUMBER SEQUENCES
1. Introduction
A number sequence is an ordered list of numbers governed by a pattern or rule.
Each number in a sequence is called a term.
- An infinite sequence continues indefinitely.
- A finite sequence has an end.
2. Arithmetic Sequences
An arithmetic sequence is formed by adding or subtracting a constant value.
| 1st Term | Rule | First Five Terms |
|---|---|---|
| 3 | Add 6 | 3, 9, 15, 21, 27 |
| 8 | Subtract 2 | 8, 6, 4, 2, 0 |
| 12 | Add 7 | 12, 19, 26, 33, 40 |
3. Geometric Sequences
A geometric sequence is formed by multiplying or dividing by the same number.
This number is called the common ratio.
| 1st Term | Rule | First Five Terms |
|---|---|---|
| 5 | ×2 | 5, 10, 20, 40, 80 |
| 243 | ÷3 | 243, 81, 27, 9, 3 |
| 1 | ×4 | 1, 4, 16, 64, 256 |
4. Other Sequences
- Square numbers: 1, 4, 9, 16, 25, …
- Cube numbers: 1, 8, 27, 64, 125, …
- Prime numbers: 2, 3, 5, 7, 11, …
5. Random Sequences
Some sequences do not follow a clear rule.
Exercise 1.4
a) 8, 14, 20, 26,
Common difference = +6 → 26+6=32 → 38 → 44
b) 2, 5, 8, 11,
Common difference = +3
c) 11, 15, 19, 23,
Common difference = +4
d) 7, 10, 13, 16,
Common difference = +3
e) 5, 9, 13, 17,
Common difference = +4
f) 2, 6, 18, 54,
Common ratio = ×3
g) 256, 128, 64, 32,
Common ratio = ÷2
h) 7, 8, 10, 13,
Increasing differences +1, +2, +3…
i) 10, 17, 22, 29, 34,
Alternating +7, +5
j) 56, 52, 46, 38,
Subtracting 4, 6, 8, 10…