There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.
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2 shapes are possible with 3 squares: L, I
5 shapes are possible with 4 squares: L, I, N, T, O
Y=(-1/6)x+5
m=(y2-y1)/(x2-x1)
m=(3-6)/(12-(-6))
m=(-3)/(18)
m=-1/6
y=mx+b
y=(-1/6)x+b
6=(-1/6)(-6)+b
6=1+b
b=5
y=(-1/6)x+5
To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.