Question

If f(1) 10 and f(n) = 2 f(n-1) then find the value of f( 6).

Answer 1

`\begin{gathered} f(1)=10 \\ f(n)=2f(n-1) \end{gathered}`

To find f(6) we first have to find the value of f(5). To find f(5) we have to find we have to find f(4), and so on. With this in mind we have:

`\begin{gathered} f(2)=2f(2-1)=2f(1)=2\cdot10=20 \\ f(3)=2f(3-1)=2f(2)=2\cdot20=40 \\ f(4)=2f(4-1)=2f(3)=2\cdot40=80 \\ f(5)=2f(5-1)=2f(4)=2\cdot80=160 \\ f(6)=2f(6-1)=2f(5)=2\cdot160=320 \end{gathered}`

Therefore, f(6)=320.