Total number of squares in pattern 100 is 303.
What is a square pattern?
Square pattern represents squares stacked on top of each other to achieve a unique pattern.
Let the number of squares in the pattern n is [tex]p_{n}[/tex] then we know
[tex]P_{n+1}-P_{n}=3, P_{1}=6[/tex]
So, [tex](P_{n}-P_{n-1})+(P_{n-1}-P_{n-2})+.......+(P_{2}-P_{1})=3 \times (n-1) = 3n - 3[/tex]
Which is [tex]P_{n}-P_{1} =3n-3[/tex]
So, [tex]P_{n}-6=3n-3[/tex]
[tex]P_{n} =3n+3[/tex]
So, [tex]P_{100} =3 \times 100+3[/tex]
[tex]P_{100} =300 +3[/tex]
[tex]P_{100} =303[/tex]
Total number of squares in pattern 100 is 303.
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