Answer:
[tex]a_n=(-2)^{n-1}[/tex]
Step-by-step explanation:
So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values
Plug known values in:
[tex]-8 = a_1(-2)^{4-1}[/tex]
Subtract the values in the exponent
[tex]-8 = a_1(-2)^3[/tex]
Simplify the exponent
[tex]-8 = a_1 (-8)[/tex]
Divide both sides by -8
[tex]1=a_1[/tex]
So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]
