Answer
$32768$.
Work Step by Step
The number of ancestors in each level is the geometric sequence: $2,2^2,2^3,...$.
The general formula for a geometric sequence is:
$a_n=a_{1}r^{n-1}$
where $r$ is the common ratio and $a_1$ is the first term. Here, $a_1=2$ and $r=2$, so we have:
$a_n=2(2)^{n-1}$
To find the number of ancestors $15$ generations back, we use $n=15$:
$a_{15}=2(2)^{15-1}=2(2)^{14}=2^{15}=32768$
