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Directions for the below question:

Let $a_1=p$ and $b_1 =q$ where $p$ and $q$ are positive quantities.

Define:

$a_n pb_{n-1} \: \: \: b_n=qb_{n-1}$ for even $n>1$

and $a_n pa_{n-1} \: \: \: b_n=qa_{n-1}$ for odd $n>1$

If $p=1/3$ and $q= 2/3,$ then what is the smallest odd $n$ such that $a_n + b_n < 0.01$?

1. $7$
2. $13$
3. $11$
4. $9$
5. $15$

1
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