Answer
Answer $D$: $1.59\text{ billion}$
Work Step by Step
Let $a_n$ be the number of cassettes shipped in US $n-1$ years after $1994$. The series is geometric with $a_1=345$ and ratio $r=1-0.217=0.783$.
The total number of cassettes shipped from $1994$ onward is:
$$S=\sum_{n=1}^{\infty}345(0.783)^{n-1}.$$
Because the ratio verifies $|r|=|0.783|<1$ the sum is:
$$S=\dfrac{a_1}{1-r}=\dfrac{345}{1-0.783}=\dfrac{345}{0.217}\approx 1590\text{ million}=1.59\text{ billion}$$
The correct answer is Answer $D$.
