lizr2002
contestada

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.
-1, -4, -16, -64 .....

Respuesta :

dexteright02
Here we have a geometric progression!

Data:
n (Number of terms) = 8
[tex] a_{8} = ?[/tex] (eighth term)
r (common ratio) = ? 
a1 (first term) = - 1
a2 second term) = - 4

If: [tex]r = \frac{ a_{2} }{ a_{1} } = \frac{-4}{-1} \to\:\boxed{r= 4}[/tex]

Now, find the geometric progression
Formula:
[tex] a_{n} = a_{1} *r^{n-1}[/tex]

Solving:
[tex] a_{n} = a_{1} *r^{n-1}[/tex]
[tex]a_{8} = -1 *4^{8-1}[/tex]
[tex]a_{8} = -1 *4^{7}[/tex]
[tex]a_{8} = -1 *16384[/tex]
[tex]\boxed{\boxed{a_{8} = -16384}}\end{array}}\qquad\quad\checkmark[/tex]

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