Question

Fill in the blanks pls, ignore the ones inside it

Answer 1

For n=0, we have

`f(0)=3`

for n=1, we have

`\begin{gathered} f(1)=2f(0) \\ f(1)=2\cdot3=6 \end{gathered}`

for n=2, we obtain

`\begin{gathered} f(2)=2f(1) \\ f(2)=2\cdot6=12 \end{gathered}`

for n=3, we have

`\begin{gathered} f(3)=2f(2) \\ f(3)=2\cdot12=24 \end{gathered}`

and so on. Then, the pattern is given by

`\begin{gathered} f(n)=3\cdot2^n\text{ for n}\ge1 \\ \text{with f(0)=3} \end{gathered}`

Lets check our formula.

When n=1, we have

`f(1)=3\cdot2=6`

when n=2, we have

`f(2)=3\cdot2^2=3\cdot4=12`

when n=3, we have

`f(3)=3\cdot2^3=3\cdot8=24`