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A sequence of patterns uses grey squares and white squares here are the first four patterns workout the total number of squares in pattern 100 3 marks

A Sequence Of Patterns Uses Grey Squares And White Squares Here Are The First Four Patterns Workout The Total Number Of Squares In Pattern 100 3 Marks class=

Sagot :

Answer:

100

Step-by-step explanation:

if pattern 1 has 1 shade, pattern 2 has 2 shades, pattern 3 has 3 shades, and so on... therefore, pattern 100 has 100 shades of grey.

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.

Find out more information square pattern here

https://brainly.com/question/16977578

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