Evaluate sequences in recursive form. f(1)=3 , f(n)=f(n-1)+5.5

Answer 1

We usually write recursive formulae this way:

f(n+1)=f(n)+5.5

Δ f(n)=5.5 => f(n) = 5.5n + C and

3=5.5*1 + C => C=-1.5

f(n)=5.5n - 1.5

The third line in my answer is called a difference equation.

Difference equations, like differential equations have known general solutions.

The form with the Δ in it says that the first difference of the function f is constant which means that the function itself is linear.