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The diagram shows a sequence of three squares made with matches. Work out the rule to give the number of matches needed to make the nth square in the sequence.

The diagram shows a sequence of three squares made with matches Work out the rule to give the number of matches needed to make the nth square in the sequence class=

Respuesta :

bekkarmahdi702

Answer:

below

Step-by-step explanation:

Notice that each time we add a an odd number of squares  to create a new square

  • 1 ⇒ 4(3+1) ⇒ 9(4+5)

each time we add an odd number we create a perfect square

a perfect square.

  • the first square has only one small square ( [tex]\sqrt{1} = 1[/tex])
  • the second one has 4 small squares ( [tex]\sqrt{4} = 2[/tex])
  • the third has 9 squares ( [tex]\sqrt{9} =3[/tex])

A perfect square is written as:

  • P = n²
  • P is the perfect square
  • n is a positive integer ( since we are working with squares)

to get the first square we replaced n with 1, to get the second one we replaced it with two and so on ...

So the formula is:

  • [tex]P = n^{2}[/tex]

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