Each stroke of a pump removes 8.2% of the remaining air from a container. What percent of the air remains after 50 strokes?

I originally thought this was simple, use the formula $\displaystyle a_n=a_1r^{n-1}$

where

$\displaystyle a_1=1$

$\displaystyle r=0.918$

and $\displaystyle n=50$

substituting in these values i get

$\displaystyle a_{50}=1*0.918 ^{50-1}$

$\displaystyle a_{50}=0.015111$

and therefore ~1.51%

however, the solution in my textbook shows the intermediary step to be

$\displaystyle a_{50}=1*0.918 ^{50}$

and final solution as

$\displaystyle a_{50}=0.01387$

Which brings me to my main question: Could somebody explain to me why the textbook's solution shows $\displaystyle 0.918^{50}$ instead of $\displaystyle 0.918^{50-1}$? Is it something to do with $\displaystyle a_{1}=1$? a mistake in the book? or something else?

thanks in advance