How many squares in the 1000th figure?

jnfisher

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Suppose the sequence of figures shown continues as established by these first four figures. Determine the amount of grey squares that would compromised the 1000th figure?

Figure 1: 1 square
Figure 2: 5 squares
Figure 3: 13 squares
Figure 4: 25 squares

How many squares in Figure 1000?
 
Can you please show us any partial work you've done on this problem? Put it down even if you're sure it's wrong, as then we can know how best to help you. At this point, the best I can offer you is a small hint on how to get started...

The number of squares in any figure can be represented by the function f(x). So, to find f(1000), you'll need to find the pattern and then solve for the 1000th value. Do you notice a pattern in the four given values? Are they growing at a fixed rate?
 
Suppose the sequence of figures shown continues as established by these first four figures.
Is there some sort of drawing that goes along with this textual exercise, to which the textual portion refers as "figures"? If so, you'll need to provide a detailed description of that graphic, or else post the graphic itself.

Determine the amount of grey squares that would compromised the 1000th figure?

Figure 1: 1 square
Figure 2: 5 squares
Figure 3: 13 squares
Figure 4: 25 squares

How many squares in Figure 1000?
What is the point of squares being "gray"? Are there other squares, of other colors? Are the gray squares part of something else?

When you reply, please include a clear listing of your thoughts and efforts so far. Please be complete. Thank you! ;)
 
Denis's algorithm (non-recursive) is faster for this problem.....
 
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