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2025 SSMO Speed Round Problems/Problem 1

Revision as of 11:09, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Define <cmath>f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ x^2 + 1 & \text{if } x \geq 0 \end{cases}</cmath> and let <math>x_0 = -3</math>. Define <math>x_{n+...")
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Problem

Define \[f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ x^2 + 1 & \text{if } x \geq 0 \end{cases}\] and let $x_0 = -3$. Define $x_{n+1} = f(x_n)$. Find the least $n$ such that $x_n > 100$.

Solution

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