Question

F(n) = -11 + 22(n - 1)Complete the recursive formula of f(n).f(1) = f(n) = f(n - 1) +

Answer 1

F(n) = -11 + 22(n-1)

`\begin{gathered} f(1)\text{ implies that n=1} \\ F(1)\text{ = -11+22(1-1)} \\ f(1)=-11 \end{gathered}`

Hence F(1) = -11

`\begin{gathered} f(n-1)\text{ implies n=n-1} \\ f(n-1)=-11\text{ +22(n-1-1)} \\ f(n-1)=-11+22(n-2)_{} \\ =\text{ -11+22n-44} \\ f(n-1)=22n-55 \end{gathered}`
`\begin{gathered} f(n)=\text{ -11+22(n-1)} \\ =-11+22n-22 \\ 22n-33 \\ \end{gathered}`

let An = F(n) -F(n-1)

`\begin{gathered} 22n-33\text{ - (22n-55)} \\ 22n\text{ - 33-22n+55} \\ =-33+55 \\ =22 \end{gathered}`

Hence F(n)= f(n-1) +22