At stage 20, you mentioned there are \(2^{10}\) circles.
To find the number of circles at stage 21, we can assume that the pattern continues similarly. If the pattern is that each stage doubles the number of circles from the previous stage, then at stage 21, there would be:
\[ 2^{11} , \text{circles (since} , 2^{11} = 2 \times 2^{10}\text{)} \]
Now, to compare the number of circles at stage 21 to stage 20:
\[ \frac{2^{11}}{2^{10}} = 2 \]
This means there will be 2 times as many circles at stage 21 compared to stage 20.
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