posted by Brittany on .
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?
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.
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