Question

Explicit formula for geometric

Answer 1

Remark
What you have to do to learn the difference between recursive and explicit is try try the first 3 or 4 terms to see what you have and how you did it.

a1 = - 3
a2 = - 3 (1/8) = -3 / 8

a3 =  (a2) (1/8)
a3 =  (-3/8) * 1/8
a3 =  (- 3/64)

a4 =  a3 (1/8)
a4 = -3/64 * 1/8
a4 = - 3 / 512  

Take a good look at a4. What do you notice? No matter what, you are always multiplying by 1/8. That means that A and D are both wrong which they would have you raising by 3 or - 3 to some power.

So which one of B and C is correct?
The answer is which ever one will not change sign from what it started out with. All four terms are minus. 

In B the term is multiplied by plus 1/8. That will not change the sign of the next term.

So the answer is
a_n = - 3 * (1/8)^(n - 1) <<<<< answer