Question

What is the recursive formula for the geometric sequence with this explicit formula

Answer 1

Answer:

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

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

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

where,

$a_1$ is the first term

r is the common ratio to the following terms.

As per the statement:

Given the explicit formula for geometric sequence:

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

On comparing with [1] we have;

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

The recursive formula for geometric sequence is given by:

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

Substitute the given values we have;

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

Therefore, the recursive formula for the geometric sequence is, $a_n = a_{n-1} \cdot (-\frac{1}{3})$

Answer 2

Answer:

a_0 = -27

a_n = a_(n-1) * (-1/3)

Step-by-step explanation:

First evaluate given formula at n=0 and specify that as starting value

Then find how to get from n-1 to n by comparing two values. In this case the next value is formed by multiplying by -1/3.