Respuesta :

konrad509
It's geometric sequence where [tex]a_1=12, q=-\dfrac{1}{2}[/tex]

So [tex]a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}[/tex]

Answer:

[tex]a_n=12*(-\frac{1}{2})^{n-1}[/tex]

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 [tex]a_n=a_1*r^{n-1}[/tex], where,

[tex]a_n=\text{ nth term of sequence}[/tex],

[tex]a_1=\text{ 1st term of sequence}[/tex],

[tex]r[/tex] = Common ratio.

[tex]n[/tex] = Number of terms of sequence.

To find common ratio, we will divide any term of our given sequence by its previous term.

[tex]r=-\frac{-6}{12}=-\frac{1}{2}[/tex]

[tex]a_n=12*(-\frac{1}{2})^{n-1}[/tex]

Therefore, our required formula would be [tex]a_n=12*(-\frac{1}{2})^{n-1}[/tex].