Question

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.

Answer 1

below

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 (
  `√(1) = 1`)
• the second one has 4 small squares (
  `√(4) = 2`)
• the third has 9 squares (
  `√(9) =3`)

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:

• 
  `P = n^(2)`