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,

$1,\frac{2}{3},\ldots.$

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

$c(5)=c(1)+(5-1)\times-\frac{1}{3}$

Therefore,

$\begin{gathered} c(5)=1-\frac{4}{3} \\ =-\frac{1}{3} \end{gathered}$

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