# O

Algebra Level 5

There exists a sequence whose terms are $$a_{1}, a_{2}, \ldots, a_{72}$$ satisfying the following conditions:

(1): $${ a }_{ i }\in \left\{ { 0 },{ 1 } \right\}$$ for all $$1 \le i \le 72$$

(2): $${ a }_{ i+9 }+{ a }_{ i+10 }+\cdots+{ a }_{ i+16 }>{ a }_{ i+1 }+{ a }_{ i+2 }+\cdots+{ a }_{ i+8 }$$ for all $$0 \le i \le 56$$.

Find the value of $$a_{38}$$.

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