Question

Which closed form definition produces the same sequence as g(n) = g(n-1) + 2 where g(1) = 5?

Answer 1

We have that

`g(n)=g(n-1)+2`

then

`\begin{gathered} g(2)=g(1)+2 \\ g(3)=g(2)+2=g(1)+2+2=g(1)+4 \\ g(4)=g(3)+2=g(1)+4+2=g(1)+6 \\ \ldots \end{gathered}`

so, we see that a closed-form is

`\begin{gathered} f(x)\text{ = g(1)+2(x-1)} \\ f(x)=5+2x-2 \\ f(x)=2x+3 \end{gathered}`

Then, the answer is the second one