Question

For the following geometric sequence find the explicit formula. {12, -6, 3, ...}

Answer 1

It's geometric sequence where $a_1=12, q=-\dfrac{1}{2}$

So $a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}$

Answer 2

Answer:

$a_n=12*(-\frac{1}{2})^{n-1}$

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 $a_n=a_1*r^{n-1}$, where,

$a_n=\text{ nth term of sequence}$,

$a_1=\text{ 1st term of sequence}$,

$r$ = Common ratio.

$n$ = Number of terms of sequence.

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

$r=-\frac{-6}{12}=-\frac{1}{2}$

$a_n=12*(-\frac{1}{2})^{n-1}$

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