You may use a calculator in this activity.

This activity is about Mathematical Matt, who asks his parents:

*"Let's change how much pocket money I get! How about you give me 1p the first week, 2p the second week, 4p the third week, 8p in week 4, 16p in week 5 and so on...?"*

Here's the weekly amount in pence:

1 2 4 8 16 ...

Starting at 1, we get the next number by **multiplying by 2** or **doubling the previous number**.

These numbers are also called the **powers of 2**.

Week 1... 2^{0} = 1

Week 2... 2^{1} = 2

Week 3... 2^{2} = 4

Week 4... 2^{3} = 8

Week 5... 2^{4} = 16

The** 'powers of 2' **are an example of a **geometric **sequence, where each term after the first is found by multiplying the previous term by a fixed number, called the common ratio. The common ratio is 2.

The powers of 2 sequence goes on forever - it is infinite and grows quickly!

**Example 1**

How much will Matt get, in pence, in week 7?

**Answer**

He will get 2^{6} = **64p**.

**Example 2**

How much will Matt get, in pence, in total by week 4?

**Answer**

He will get 1 + 2 + 4 + 8 =** 15p**.

**Example 3**

How much will Matt get, in pounds, in **week 17**?

**Answer**

He will get 2^{16} =** **65,536p =** £655.36**.

Shall we get started?