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.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- term
- one of the numbers in the pattern
- common difference
- the fixed amount added each step
- position
- which term it is — 1st, 2nd, 3rd, …
Worked examples
2, 5, 8, 11, … 6th term
- 1.Goes up by 3.
- 2.2 + 5 × 3 = 2 + 15 = 17.
= 17
3, 7, 11, 15, … 6th term
- 1.Goes up by 4.
- 2.3 + 5 × 4 = 3 + 20 = 23.
= 23
1, 3, 5, 7, … 7th term
- 1.Goes up by 2.
- 2.1 + 6 × 2 = 1 + 12 = 13.
= 13
For parents
Method: Count the jumps between terms.
What to say: Ask 'how much does it go up each time?' then 'how many jumps to get there?'
Common mistakes:
- Making one jump too many (using the position instead of position − 1).
- Giving the common difference as the answer, or forgetting the starting term.