Here we have a geometric progression!
Data:
n (Number of terms) = 8
\(a_{8} = ?\) (eighth term)
r (common ratio) = ?
a1 (first term) = - 1
a2 second term) = - 4
If: \(r = \frac{ a_{2} }{ a_{1} } = \frac{-4}{-1} \to\:\boxed{r= 4}\)
Now, find the geometric progression
Formula:
\(a_{n} = a_{1} *r^{n-1}\)
Solving:
\(a_{n} = a_{1} *r^{n-1}\)
\(a_{8} = -1 *4^{8-1}\)
\(a_{8} = -1 *4^{7}\)
\(a_{8} = -1 *16384\)
\(\boxed{\boxed{a_{8} = -16384}}\end{array}}\qquad\quad\checkmark\)
