Answer :
We start by using the formula for the \( n \)th term of a geometric sequence:
$$
a_n = a_1 \cdot r^{n-1}.
$$
1. Given that \( a_1 = 4 \) and \( a_8 = -8748 \), we have:
$$
a_8 = 4 \cdot r^{7} = -8748.
$$
2. Solve for \( r^7 \):
$$
r^{7} = \frac{-8748}{4} = -2187.
$$
3. Notice that
$$
-2187 = -3^7,
$$
so it follows that
$$
r = -3.
$$
4. To find the 16th term, use the formula with \( n = 16 \):
$$
a_{16} = 4 \cdot (-3)^{15}.
$$
5. Since
$$
(-3)^{15} = -3^{15} = -14348907,
$$
we have:
$$
a_{16} = 4 \cdot \left(-14348907\right) = -57395628.
$$
Thus, the 16th term is
$$
\boxed{-57395628}.
$$
This corresponds to option b.
$$
a_n = a_1 \cdot r^{n-1}.
$$
1. Given that \( a_1 = 4 \) and \( a_8 = -8748 \), we have:
$$
a_8 = 4 \cdot r^{7} = -8748.
$$
2. Solve for \( r^7 \):
$$
r^{7} = \frac{-8748}{4} = -2187.
$$
3. Notice that
$$
-2187 = -3^7,
$$
so it follows that
$$
r = -3.
$$
4. To find the 16th term, use the formula with \( n = 16 \):
$$
a_{16} = 4 \cdot (-3)^{15}.
$$
5. Since
$$
(-3)^{15} = -3^{15} = -14348907,
$$
we have:
$$
a_{16} = 4 \cdot \left(-14348907\right) = -57395628.
$$
Thus, the 16th term is
$$
\boxed{-57395628}.
$$
This corresponds to option b.
