# Mathematrics

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Each diagram in the sequence is obtained by drawing of a 1 unit square on each side that forms the perimeter of the previous diagram, the 1st digram contains (1) square, the 2nd diagram (4) squares and the 3rd diagram (13) squares, I would like to know how to find how many squares will be in the fourth diagram? and what are the appropriate values for the rows marked 1st, 2nd and 3rd?

• Mathematrics -

shouldnt the 2nd diabram have 5 squares.
I believe the CHANGE in the number of squares grows by 4 each time. So, 1, 5, 13, 25, and so on.

• Mathematrics -

or

the total number of squares after n stages is

2n^2 - 2n + 1

test: if n= 4
we get 2(16) - 8 + 1 = 25
as economyst predicted

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