Question

Question 10 of 10 What is the recursive formula for the geometric sequence with this explicit formula? •(-3) la = 9 O A. OA, an ar-1 0 la = -9 = O B. an = an-1 . im 3 OC. 3 a = an-1 • (-9) (2, - - 1/2 a 3

Answer 1

Given the explicit formula for the Geometric Sequence:

$a_n=9\cdot(-\frac{1}{3})^{(n-1)}$

Where the nth term is:

$a_n$

Then, you need to remember that, by definition, the Recursive Formula for a Geometric Sequence has this form:

$a_n=a_{n-1}\cdot r$

Where "r" is the common ratio.

In this case, having the explicit formula with the form:

$a_n=a_1\cdot r^{(n-1)}$

You can identify that:

$r=-\frac{1}{3}$$a_1=9$

Therefore, you can set up the following recursive formula:

$a_n=a_{n-1}(-\frac{1}{3})$

Hence, you get:

$\begin{cases}a_1=9_{} \\ \\ a_n=a_{n-1}(-\frac{1}{3})\end{cases}$

Therefore, the answer is: Option A.