Number Sequences: Finding the Rule and Next Term
A number sequence is an ordered list of numbers following a specific pattern or rule, often involving consistent addition or subtraction.
- Main query
- number sequences
- Related searches
- linear number sequences, linear sequences
A number sequence is an ordered list of numbers that follows a specific pattern or rule. Understanding these rules is a key skill for 11+ exams, helping you predict future terms in the sequence.
A linear number sequence is a common type where the difference between consecutive terms remains constant. This constant difference is the ‘rule’ of the sequence, which can involve adding or subtracting the same number each time.
To find the rule in a sequence, look at the difference between the first two numbers, then the second and third, and so on. If this difference is always the same, you've found the rule. For example, in 3, 6, 9, 12, the rule is ‘add 3’.
Once you've identified the rule, finding the next term in a sequence is straightforward. Simply apply the rule to the last given number. If the rule is ‘add 3’ and the last term is 12, the next term will be 12 + 3 = 15.
Check Understanding
What is a **number sequence**?
Answer
An ordered list of numbers following a specific pattern or rule.
Why it works
In 11+ maths, these often involve consistent addition or subtraction between terms, forming a linear number sequence.
Find the rule and the next term for the sequence: 4, 9, 14, 19, ...
Answer
The rule is ‘add 5’. The next term is 24.
Why it works
Look at the difference between consecutive terms: 9-4=5, 14-9=5, 19-14=5. The constant difference is +5. So, 19 + 5 = 24.
Are all number sequences linear?
Answer
No, some sequences follow other rules like multiplication or adding previous terms.
Why it works
A linear number sequence has a constant difference between terms. Other sequences, like 2, 4, 8, 16 (multiply by 2) or 1, 1, 2, 3, 5 (Fibonacci, add the two previous terms), are not linear.
A sequence starts with 10, 8, 6. What is the 5th term?
Answer
The 5th term is 2.
Why it works
The rule is ‘subtract 2’ (10-8=2, 8-6=2). The terms are 10, 8, 6, 4 (6-2), 2 (4-2).
Examples
Find the rule and the next term for: 2, 5, 8, 11, ...
The difference between each term is +3. So, the rule is ‘add 3’. The next term is 11 + 3 = 14.
Find the rule and the next term for: 20, 18, 16, 14, ...
The difference between each term is -2. So, the rule is ‘subtract 2’. The next term is 14 - 2 = 12.
Quick Answers
What is a linear number sequence?
It's a sequence where the difference between consecutive terms is always the same, either by adding or subtracting a constant number.
How do I find the rule for a sequence?
Look at the difference between each pair of consecutive numbers. If this difference is constant, that's your rule. If not, look for other patterns like multiplication.
Are all number sequences linear?
No, some sequences have rules that involve multiplication, division, or more complex patterns (e.g., Fibonacci sequence where you add the two previous terms).