The rule which give the number of dots for the nth figure is [tex]= n^{2}[/tex] or number of dots [tex]= n \times n[/tex], where n represents the number of figure.
What is pattern?
A pattern is a repeated arrangement of numbers, shapes, colors and so on.
Let n represents the number of figure and m be the number of dots.
According to the given question.
We have some figures which is made up of dots with following some patterns.
In the given first figure i.e. for n = 1
The total number of dots is 1.
[tex]\implies m = 1[/tex]
In the second figure i.e. for n = 2
The number of dots gets increased and the counts of dots are 4.
⇒ [tex]m = 4[/tex]
[tex]\implies m = 2 \times 2[/tex]
In the third figure i.e. for n = 3.
The number of dots are 9
[tex]\implies m = 9[/tex]
[tex]\implies m = 3 \times 3[/tex]
Similarly, for the nth figure, the number of dots is given by
[tex]m = n \times n[/tex]
[tex]\implies m = n^{2}[/tex]
Hence, the rule which give the number of dots for the nth figure is number of dots [tex]= n^{2}[/tex] or number of dots [tex]= n \times n[/tex], where n represents the number of figure.
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