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In this worksheet, students use the powers of 2 as a geometric sequence to work out problems involving doubling of pocket money.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Geometric Sequences

Difficulty level:

QUESTION 1 of 10

You may use a calculator in this worksheet.

This worksheet is about Mathematical Matt, who says to 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 are the amounts 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 for ever. It is infinite and grows quickly!

Example 1

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

He will get 26 = 64p.

Example 2

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

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

Example 3

How much will Matt get, in pounds, in Week 17?

He will get 216 = 65 536p = £655.36.

How much will Matt get, in pence, in Week 6?

Just write the number.

How much will Matt get, in pence, in Week 8?

Just write the number.

How much will Matt get, in pence, in total by Week 5?

Just write the number.

How much will Matt get, in pounds, in total by Week 8?

Just write the number.

How much will Matt get, in pounds, in Week 10?

Just write the number.

In which week will Matt receive £2.56?

Just write the number of the week.

In which week will Matt receive more than £10 for the first time?

Just write the number of the week.

How much will Matt get, in pounds, in Week 15?

Just write the number.

How much will Matt get, in pounds, in Week 26?

Just write the number.

In which week will Matt receive more than a million pounds for the first time?

(Ignore the previous amounts he has received.)

• Question 1

How much will Matt get, in pence, in Week 6?

Just write the number.

32
EDDIE SAYS
25 = 32p
• Question 2

How much will Matt get, in pence, in Week 8?

Just write the number.

128
EDDIE SAYS
27 = 128p
• Question 3

How much will Matt get, in pence, in total by Week 5?

Just write the number.

31
EDDIE SAYS
1 + 2 + 4 + 8 + 16 = 31p
• Question 4

How much will Matt get, in pounds, in total by Week 8?

Just write the number.

2.55
EDDIE SAYS
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255p = £2.55
• Question 5

How much will Matt get, in pounds, in Week 10?

Just write the number.

5.12
EDDIE SAYS
29 = 512p = £5.12
• Question 6

In which week will Matt receive £2.56?

Just write the number of the week.

9
EDDIE SAYS
28 = 256p = £2.56
• Question 7

In which week will Matt receive more than £10 for the first time?

Just write the number of the week.

11
EDDIE SAYS
210 = 1024p = £10.24
• Question 8

How much will Matt get, in pounds, in Week 15?

Just write the number.

163.84
EDDIE SAYS
214 = 16 384p = £163.84
• Question 9

How much will Matt get, in pounds, in Week 26?

Just write the number.

335544.32
335 544.32
EDDIE SAYS
225 = 33554432p = £335 544.32
• Question 10

In which week will Matt receive more than a million pounds for the first time?

(Ignore the previous amounts he has received.)

28
EDDIE SAYS
226 = 67108864p = £671 088.64
227 = 134217728p = £1 342 177.28
---- OR ----

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