D
the n th term (explicit ) formula for a geometric sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]
The given explicit formula therefore has
[tex]a_{1}[/tex] = 5 and r = - [tex]\frac{1}{8}[/tex]
The recursive formula, allows us to find the next term in the sequence from the previous term
Here the next term in the sequence is obtained by multiplying the previous term by - [tex]\frac{1}{8}[/tex]
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex](- [tex]\frac{1}{8}[/tex]) with [tex]a_{1}[/tex] = 5
