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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

Respuesta :

Let the full cake represent,

[tex]c(1)=1[/tex]

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

[tex]1,\frac{2}{3},\ldots.[/tex]

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

[tex]c(5)=c(1)+(5-1)\times-\frac{1}{3}[/tex]

Therefore,

[tex]\begin{gathered} c(5)=1-\frac{4}{3} \\ =-\frac{1}{3} \end{gathered}[/tex]

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

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