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Doubling map sequence term

High school · ●●○○○ 20 pts

A sequence {an}\{a_n\} satisfies an+1=2ana_{n+1}=2a_n if 0⩽an<120 \leqslant a_n < \frac{1}{2} and an+1=2an−1a_{n+1}=2a_n-1 if 12⩽an<1\frac{1}{2} \leqslant a_n < 1, for every positive integer nn, and a1=67a_1=\frac{6}{7}. Find a24a_{24}. Round to two decimal places.

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recurrence relationsperiodic functionspiecewise functions