Question

what is an explicit equation for:f(n)=5+ f(n-1);f(1)=0

Answer 1

Substitute 2 for n in the equation .

$\begin{gathered} f(2)=5+f(2-1) \\ f(2)=5+f(1) \\ f(2)=5+0 \\ =5 \end{gathered}$

Determine the common difference for the sequence.

$\begin{gathered} d=f(2)-f(1) \\ =5-0 \\ =5 \end{gathered}$

So commons difference is 5.

The general explict equation is,

$a_n=a_1+(n-1)d$

Determine the explicit equation for the given recursive relation.

$\begin{gathered} a_n=0+5(n-1) \\ =5(n-1) \end{gathered}$

So explicit equation is,

$a_n=5(n-1)$