# Powers of 2

In this worksheet, students work with the powers of 2 as an example of a geometric sequence. Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Sequences

Difficulty level:   ### QUESTION 1 of 10

Here is a sequence of numbers:

1,   2,   4,   8,   16,   32,   64,   128...

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.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

... etc...

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!

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, ?, 16, 32, ...

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, ?, 64, ...

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, ?, ...

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, ?, ...

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, 128, ?, ...

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, 128, 256, ?, ...

Is the following number a power of 2?

33

yes

no

Is the following number a power of 2?

127

yes

no

Is the following number a power of 2?

1024

yes

no

Is the following number a power of 2?

2044

yes

no

• Question 1

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, ?, 16, 32, ...

8
EDDIE SAYS
Double 4 or halve 16.
• Question 2

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, ?, 64, ...

32
EDDIE SAYS
Double 16 or halve 64.
• Question 3

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, ?, ...

64
EDDIE SAYS
Double 32.
• Question 4

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, ?, ...

128
EDDIE SAYS
Double 64.
• Question 5

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, 128, ?, ...

256
EDDIE SAYS
Double 128.
• Question 6

Work out the missing term in this 'powers of 2' sequence:

1, 2, 4, 8, 16, 32, 64, 128, 256, ?, ...

512
EDDIE SAYS
Double 256.
• Question 7

Is the following number a power of 2?

33

no
EDDIE SAYS
All powers of 2 after the first are even.
• Question 8

Is the following number a power of 2?

127

no
EDDIE SAYS
128 is a power of 2, so 127 cannot be.
127 is odd.
• Question 9

Is the following number a power of 2?

1024

yes
EDDIE SAYS
... 64, 128, 256, 512, 1024, ...
• Question 10

Is the following number a power of 2?

2044

no
EDDIE SAYS
... 64, 128, 256, 512, 1024, 2048, ...
---- OR ---- 