Answer:
![a_n=12*(-\frac{1}{2})^{n-1}](https://tex.z-dn.net/?f=a_n%3D12%2A%28-%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D)
Step-by-step explanation:
We are asked to write an explicit formula for the given geometric sequence.
We know that explicit formula for a given geometric sequence is in form
, where,
,
,
= Common ratio.
= Number of terms of sequence.
To find common ratio, we will divide any term of our given sequence by its previous term.
![r=-\frac{-6}{12}=-\frac{1}{2}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B-6%7D%7B12%7D%3D-%5Cfrac%7B1%7D%7B2%7D)
![a_n=12*(-\frac{1}{2})^{n-1}](https://tex.z-dn.net/?f=a_n%3D12%2A%28-%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D)
Therefore, our required formula would be
.