Respuesta :
Answer:
The explicit formula for a given geometric sequence is of the form
[tex]a_{4} =\frac{1}{(a_{1})^4}[/tex]
Step-by-step explanation:
Given sequence is [tex]{\{-2,6,-18,54}\}[/tex]
Let [tex]a_{1}=-2,a_{2}=6,a_{3}=-18,a_{4}=54[/tex]
To find the common ratio r:
[tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]=\frac{6}{-2}[/tex]
[tex]=-3[/tex]
Therefore r=-3
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]=\frac{-18}{6}[/tex]
[tex]=-3[/tex]
Therefore r=-3
Therefore common ratio is -3
Therefore given sequence is geometric sequence.
The explicit formula for a geometric sequence is [tex]a_{n}=a_{1}^{r-1}[/tex], where common ratio is r.
From given sequence we are having r=-3
Therefore the explicit formula for a given geometric sequence is of the form [tex]a_{4} =a_{1}^{-3-1}[/tex]
[tex]a_{4} =a_{1}^{-4}[/tex]
[tex]a_{4} =\frac{1}{(a_{1})^4}[/tex]
