Sequences
A sequence is a list of numbers that follows a rule. In a linear (arithmetic) sequence the difference between terms is always the same. The nth-term rule lets you find any term without listing them all.
Key facts
- Term-to-term rule: what you do to get from one term to the next.
- Linear: nth term = difference × n + (first term − difference).
- To check if a number is in the sequence, set the nth term equal to it and see if n is a whole number.
Worked examples
Example 1
Find the nth term of 5, 8, 11, 14, …
- It goes up by 3 each time, so it starts with 3n. 3n: 3, 6, 9, 12
- Each term is 2 more than 3n. 3n + 2
Answer: 3n + 2
Example 2
Is 100 in the sequence 3n + 2?
- Set the rule equal to 100. 3n + 2 = 100
- Solve. 3n = 98, n = 32.67
- n isn’t a whole number, so 100 is not in the sequence.
Answer: No
Example 3
Pattern 1 has 4 matches, pattern 2 has 7, pattern 3 has 10. How many matches in pattern 20?
- Up 3 each time, starting at 4. 3n + 1
- Put in 20. 3 × 20 + 1 = 61
Answer: 61