Number Sequences & Number Patterns are maths skills that are often tested in 11+ exams and Selective School exams in the UK. This includes: “Find the Rules” in diagrams and numbers to the nth degree.

## Examples

### Example Question 1:

Find the missing numbers in these number sequences:

(a) 0.01, 0.1, 1.0, 10, 100, ? , ?

(b) 25, 36, ? , 64, 81, ?

(c) 4, 5, 9, 14, 23, 37, ?

**Answers:**

(a) 1,000 and 10,000

(b) 49 and 100

(c) 60

**Explanation:**

(a) Each number in this sequence is multiplied by 10 to find the next number.

(b) This is a square number sequence and the missing numbers are 7² = 49 and 10² = 100

(c) This is a Fibonacci sequence. The previous two numbers are added together to find the next number, so 23 + 37 = 60

### Example Question 2:

What is the 100th number in this number sequence? 4, 10, 16, 22, 28

**Answer:** 598

**Explanation:** This is a n’th term question where you have to find a number much further along in a sequence. First find an algebraic rule by finding out which times table the sequence is related to. This is found by looking at the difference between the numbers (= 6) and working out how the numbers in the six times table are related to the numbers in the sequence = × 6 and then – 2 which gives you the formula 6n – 2. Apply this to the number (or term) in the question: 100 × 6 = 600, then – 2 = 598.

## Video Tutorials

### Numbers to the nth Term

### Sequences in Maths

### Fibonacci Sequence

### Patterns to the n’th term