Patterns and rules · Usually met around P4
The nth term
Adds 3 each time? Compare with 3 × n.
How to do it
Method
Adds 3 each time? Compare with 3 × n
4, 7, 10, …: nth = 3 × n + 1; the 20th = 61
Another way
Work back to the position
61 is term (61 − 1) ÷ 3 = 20
In full
When a pattern adds the same number each time, its nth term can be said in words or as a short expression. Take 4, 7, 10, 13: it adds 3 each time, so compare it with the multiples of 3: 3, 6, 9, 12, each 1 short. In words: “the position number times 3, plus 1”; as an expression, the nth term is 3 × n + 1, where n is the position. For the 20th, put 20 in for n: 3 × 20 + 1 = 61. To find which term 61 is, work backwards: (61 − 1) ÷ 3 = 20. Once the expression is written, check it with n = 1, 2, 3: does it give 4, 7, 10?
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
7, 9, 11, 13, … The nth number is □ × n + □.
Fill in each box
Show the answer and working
Answer: 2，5
It adds 2 each time, so 2 × n; 2 × 1 = 2 needs 5 more to make 7: 2 × n + 5.
Example 2
The rule is “multiply the position number by 4, then subtract 1”. The 7th number is 29.
True or false?
Show the answer and working
Answer: False
The 7th: first 7 × 4 = 28, then subtract 1: 27.
Example 3
In a pattern, the nth number is 5 × n + 3. Which term is 53?
Show the answer and working
Answer: 10
Work backwards: 53 − 3 = 50, 50 ÷ 5 = 10: the 10th.
Practise it in the game →Patterns and rules · Free to start, unlimited questions, no download