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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... 20 = 1
Week 2... 21 = 2
Week 3... 22 = 4
Week 4... 23 = 8
Week 5... 24 = 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 26 = 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 216 = 65,536p = £655.36.
Shall we get started?
Question
/ 10Mr Shepherd
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Teacher explanation