Question

a cake is in the room, 5he first person takes 1/3 and then the second person takes 1/3 of what is left and so on, c(n) represents the amount of cake left each time find out how much cake there is after 5 people

Answer 1

Let the full cake represent,

`c(1)=1`

Therfore, the given problem is in the form of an arithmetic sequence,

`1,(2)/(3),\ldots.`

Here, n=5, d=-1/3, c(1)=1

`c(5)=c(1)+(5-1)*-(1)/(3)`

Therefore,

`\begin{gathered} c(5)=1-(4)/(3) \\ =-(1)/(3) \end{gathered}`

So, the remaining amount of cake is -1/3.