Question

Which recursive formula defines this geometric for n = 1, 2 , 3, ... ?
5,15,45,135

Answer 1

Answer:

$\huge\boxed{a_n=\left\{\begin{array}{ccc}a_1=5\\a_n=3a_{n-1}\end{array}\right}$

Step-by-step explanation:

$a_1=5\\\\a_2=15=(3)(5)=3a_1\\\\a_3=45=(3)(15)=3a_2\\\\a_4=135=(3)(45)=3a_3\\\vdots\\a_n=3a_{n-1}\\\\\text{Each next term is created by multiplying the previous term by 3}.$