Question

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

-1, -4, -16, -64 .....

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 = ( a_(2) )/( a_(1) ) = (-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`