Q:

What is the recursive formula when given the explicit formula for the following geometric sequence?a^n = 12(33)^n-1

Accepted Solution

A:
Answer:[tex]\left \{ {{a_1=12} \atop{a_n=a_{n-1}*(33)}} \right.[/tex]Step-by-step explanation:For a geometric sequence the explicit formula has the following formula:[tex]a_n=a_1(r)^{n-1}[/tex]Where [tex]a_1[/tex] is the first term in the sequence, and r is the common ratio  and [tex]a_n[/tex] is the nth term of the sequence:In this case we have the following sequence[tex]a_n = 12(33)^{n-1}[/tex]Then:[tex]a_1=12\\r=33[/tex]The recursive formula for the geometric sequence has the following formula[tex]\left \{ {{a_1} \atop {a_n=a_1*r}} \right.[/tex]Where [tex]a_1[/tex] is the first term in the sequence, and r is the common ratio  and [tex]a_n[/tex] is the nth term of the sequence:In this case the recursive formula is:[tex]\left \{ {{a_1=12} \atop{a_n=a_{n-1}*(33)}} \right.[/tex]