Question

What is the recursive formula when given the explicit formula for the following geometric sequence?

Answer 1

Answer:

$\left \{ {{a_1=12} \atop{a_n=a_{n-1}*(33)}} \right.$

Step-by-step explanation:

For a geometric sequence the explicit formula has the following formula:

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

Where $a_1$ is the first term in the sequence, and r is the common ratio  and $a_n$ is the nth term of the sequence:

In this case we have the following sequence

$a_n = 12(33)^{n-1}$

Then:

$a_1=12\\r=33$

The recursive formula for the geometric sequence has the following formula

$\left \{ {{a_1} \atop {a_n=a_1*r}} \right.$

Where $a_1$ is the first term in the sequence, and r is the common ratio  and $a_n$ is the nth term of the sequence:

In this case the recursive formula is:

$\left \{ {{a_1=12} \atop{a_n=a_{n-1}*(33)}} \right.$