Question

What is the recursive formula for the geometric sequence with this explicit formula an= 5 * (-1/8)^(n-1)

Answer 1

$a_n=5\left(-\dfrac{1}{8}\right)^{n-1}\\\\a_1=5\left(-\dfrac{1}{8}\right)^{1-1}=5\left(-\dfrac{1}{8}\right)^0=5\\\\\text{The recursive formula:}\\\\a_n=\left\{\begin{array}{ccc}a_1=5\\a_{n+1}=-\dfrac{1}{8}a_{n}\end{array}\right$