Sequences and terms
A sequence is a list of numbers or objects arranged in a definite order following a pattern. Each member of the sequence is a term. We often name them the first term, second term, third term, and so on. For example, in the sequence 5, 8, 11, 14, ... the first term is 5 and the second term is 8.
Key idea / 要点
The order matters. A sequence follows a rule, so once you know the rule you can find any term.
Common differences and ratios
Many sequences change by the same amount each time. In 5, 8, 11, 14, ... you add 3 each step, so the common difference is 3. In 3, 6, 12, 24, ... you multiply by 2 each step, so the common ratio is 2.
Worked example / 例题
Find the next two terms of 40, 34, 28, 22, ...
Difference: 34 − 40 = −6, so each term decreases by 6.
Next: 22 − 6 = 16, then 16 − 6 = 10.
The next two terms are 16 and 10.
Finding a specific term
To find a later term, keep applying the rule. For 2, 6, 18, 54, ... the rule is × 3. The fifth term is 54 × 3 = 162. Checking every step avoids mistakes, especially when the terms grow quickly.
Not every list is a sequence with a simple rule — but in Form 2 the sequences you meet always follow one clear pattern.
Remember / 记住
- A term is one number in the sequence.
- Common difference: subtract a term from the next.
- Common ratio: divide a term by the previous one.