Answer
The amount she lost on her sixth bet is $\$160$.
The total amount lost on all the six bets is $\$315$.
Work Step by Step
The situation can be represented by a geometric sequence with $a_{1} = 5$ and $r = 2$, which the general term $a_{n} = 5(2)^{n−1}$ where n is the number of losing bets.
The amount she lost on her sixth bet (n = 6) is
$a_{6} = 5(2)^{6−1} = \$160$
And, the total amount lost on all the six bets is
$\sum\limits_{n=1}^6 a_{n} = \sum\limits_{n=1}^6 5(2)^{n-1}$
= $\frac{5(1−2^6)}{(1−2)}$
= $\$315$
