<h2>Number series Test3-perfect squares-cubes</h2>

 

 Different types of number series Εxamples with detailed explanations methodologies tips and tricks.

Squares: When numbers are a series of perfect squares.

 For example: 81, 100, 121, 144, 169... 

81=9^2  100=10^2   121=11^2    144=12^2   169=13^2 

The numbers of series are perfect squares of  9, 10, 11, 12,....

 Cubes: When the numbers are a series of perfect cubes. 

For example: 512, 729, 1000...

512=8^3    729=9^3    1000=10^3

 The numbers of series are perfect cubes of  8, 9, 10,...

 

 Examples

 

Example 1 

 9, 25, 49, 81, ? 

9=3² 25=5² 49=7² 81=9² 

Theese are the perfect squares of number series

 3, 5, 7, 9, 11,... 

The next term is  11² = 121

Example 2

 In the sequence one of the term is wrong 

3600, 8100, 14200, 22500

  Select the option that has his number. 

A. 22.500  B. 14200  C.8100  D.3600

3600= 60^2

8100=90^2

22500=150^2

14200  it is not a square  of any nunber

S0 correct answer is B

*The correct number is 14400 

All the terms of series are perfect squares of series 

60, 90, 120, 150

Example 3

 In the sequence one of the term is wrong

 8000, 27000, 54000, 125000 

Select the option that has his number. 

A. 27.000 B. 54000 C 8000 D 125000.

 The first digit in each term is a cube of some number .

 27=3³

 8=2³ 

125=5³

 54  its't the cube of any number 

 So correct answer is B.

 

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Questions number series squares-cubes-two stage type series

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