algebra · Year 6 · AC9M6A01
Number pattern rules
In a growing pattern like 2, 5, 8, 11, each term is a fixed amount bigger than the one before — here it goes up by 3 each time. That fixed amount is the common difference. To find a later term without writing them all out, notice there is one fewer jump than the term number: the 6th term is 5 jumps of 3 added to the start. So 2 + 5 × 3 = 17. Count the GAPS, not the terms, and never forget to add the starting number.
Sample questions
4, 7, 10, 13, … What is the 5th term?
- The pattern goes up by 3 each time.
- The 5th term = 4 + 4 × 3.
- 4 + 12 = 16.
Answer: 16
4, 6, 8, 10, … What is the 6th term?
- The pattern goes up by 2 each time.
- The 6th term = 4 + 5 × 2.
- 4 + 10 = 14.
Answer: 14
5, 8, 11, 14, … What is the 6th term?
- The pattern goes up by 3 each time.
- The 6th term = 5 + 5 × 3.
- 5 + 15 = 20.
Answer: 20