Patterns & Relationships — Practice Worksheet — Patterns & Relationships: Finding and Generalising Rules

Part A — Finding & generalising rules

A growing pattern increases by the same amount each step. We record each position and its term in a table, then generalise the rule that links them — first in words, then using a symbol such as n for the position.

A growing matchstick-square pattern with a table of position against stick count and the generalised rule 3n plus 1. — Each new square adds 3 sticks; the single extra stick at the start is the constant.

Continue the pattern

Q1. 4, 7, 10, 13, , . What is added each time?

Q2. 40, 35, 30, , . Is this increasing or decreasing? By how much?

Position-to-term tables

Q3. Complete the table for the rule "multiply position by 2, then add 1".

Position (n)	1	2	3	4	5
Term	3	5

Q4. For the matchstick pattern in the picture (4, 7, 10, 13, …), how many sticks are at position 6? At position 10?

Generalise the rule (words, then symbols)

Q5. Write in words the rule linking each term to its position for: 5, 8, 11, 14, …

Q6. Write the same rule using n (the position number).

Q7. A pattern follows the rule 2n + 3. List the first four terms.

Create

Q8. Invent your own increasing pattern, draw the first 3 terms with counters or sticks, and write its rule in words and in symbols.