# Examples of sequences

## Challenge

Take a look at the following sequences.a) 3, 3, 5, 4, 4, 3, 5, 5, _, _, …

b) 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …

c) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, _, _, …

d) 3, 7, 11, 15, …

e) 2, 4, 8 ,16, 32, …Can you spot any patterns in them? Can you find a rule that generates them?

## Solutions

### a) 3,3,5,4,4,3,5,5,*,*

### b) 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …

- 1 is read off as “one 1”
- 11 is read off as “two 1s”
- 21 is read off as “one 2, then one 1” and so on

### c) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, _, _,

**Fibonacci sequence**. We will explore this sequence in more detail later in the week.

### d) 3, 7, 11, 15, …

**arithmetic sequence**where the difference between each numbers the same.

### e) 2, 4, 8 ,16, 32, …

**geometric sequence**where we multiply by the same number each time to get the next number.

Below are some examples of number sequences, some have a mathematical rule behind them, others do not.## Problem worksheet

Now complete question 1 from this week’s worksheet.

## Challenge

Take a look at the following sequences.a) 3, 3, 5, 4, 4, 3, 5, 5, _, _, …

b) 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …

c) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, _, _, …

d) 3, 7, 11, 15, …

e) 2, 4, 8 ,16, 32, …Can you spot any patterns in them? Can you find a rule that generates them?

## Solutions

### a) 3,3,5,4,4,3,5,5,*,*

### b) 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …

- 1 is read off as “one 1”
- 11 is read off as “two 1s”
- 21 is read off as “one 2, then one 1” and so on

### c) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, _, _,

**Fibonacci sequence**. We will explore this sequence in more detail later in the week.

### d) 3, 7, 11, 15, …

**arithmetic sequence**where the difference between each numbers the same.

### e) 2, 4, 8 ,16, 32, …

**geometric sequence**where we multiply by the same number each time to get the next number.

## Problem worksheet

Now complete question 1 from this week’s worksheet.

#### Maths Subject Knowledge: Understanding Numbers

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