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)`