Question 62313
<b>I need to find the closed form of this recursive function: a(n)= 5*a(n-1) where a(0) is the initial value?</b>

Let's look at a few terms of the series to look for the pattern:

{{{a[1]=5*a[0]}}}.
{{{a[2]=5*a[1]=5*(5*a[0])}}}.
{{{a[3]=5*a[2]=5*(5*(5*a[0]))}}}.
{{{a[4]=5*a[3]=5*(5*(5*(5*a[0])))}}}.

The pattern is that {{{a[n] = 5^n*a[0]}}}.