To express the number of circles at stage 10, we first need a bit more context regarding how the number of circles grows. Typically, a geometric sequence or a recursive formula might be involved in problems involving stages.
For example, if you are doubling the number of circles at each stage, the expression for the number of circles at stage \( n \) could be:
\[ C(n) = C(0) \times 2^n \]
where \( C(0) \) is the initial number of circles.
If you have a different pattern (for example, adding a fixed number of circles at each stage, or a different multiplying factor), then the expression will change accordingly.
For a few common cases:
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Doubling at each stage: \[ C(10) = C(0) \times 2^{10} \]
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Adding a fixed number of circles \( k \) at each stage: \[ C(n) = C(0) + k \times n \] So for stage 10: \[ C(10) = C(0) + 10k \]
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A geometric progression with different ratio: \[ C(n) = C(0) \times r^n \] So, \[ C(10) = C(0) \times r^{10} \]
If you can provide the specific pattern or rules for how the circles are growing, I can help you formulate the exact expression for stage 10.
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