Answer
$65,534$ ancestors
Work Step by Step
We model the problem using a geometric sequence $\{a_n\}$ with the elements:
$$\begin{cases}
a_1=1\\
r=2.
\end{cases}$$
To find the total number of persons in $16$ generations (which means $15$ generations after the one to which the person belongs) we calculate $S_{16}$ using the formula:
$$S_n=\dfrac{a_1(1-r^n)}{1-r}.$$
Substitute $n=16$, $a_1=1$ and $r=2$:
$$S_{16}=\dfrac{1(1-2^{16})}{1-2}=65,535.$$
To determine the number of ancestors we must take the person out of the sum:
$$S_{16}-1=65,535-1=65,534.$$
