Question

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.

Answer 1

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:
$a_{n} = a_{1} *r^{n-1}$
$a_{8} = -1 *4^{8-1}$
$a_{8} = -1 *4^{7}$
$a_{8} = -1 *16384$
$\boxed{\boxed{a_{8} = -16384}}\end{array}}\qquad\quad\checkmark$