Answer:
[tex]a_{n} = - 2^{n-1}[/tex].
Step-by-step explanation:
Given : geometric sequence -1, -2, -4, ...
To find : Which of the following represents the general equation for the geometric sequence.
Solution : We have given
Geometric sequence -1, -2, -4, ...
By the formula for general equation : [tex]a_{n} = a_{1} *r^{n-1}[/tex].
Where, [tex]a_{n}[/tex] = last term.
[tex]a_{1}[/tex] = first term.
r = common ratio.
r ( common ratio ) = [tex]\frac{second\term}{first\term}[/tex].
In -1, -2, -4, ...
[tex]a_{1}[/tex] = -1.
r ( common ratio ) = [tex]\frac{-2}{-1}[/tex].
r ( common ratio ) =2.
Plug the values in formula
[tex]a_{n} = (-1) * 2^{n-1}[/tex].
[tex]a_{n} = - 2^{n-1}[/tex].
Therefore, [tex]a_{n} = - 2^{n-1}[/tex].
