Question

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

Answer 1

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

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}.`