Stewart's Sequences 1 of 5

x(n) = 7n/3; by this calculate x(30)+x(60) = 210

Here is the sequence of pie baking and their respective values of $n$ :

$\begin{matrix} n= & 1 & 2 & 3 \\ pies= & 2\frac { 1 }{ 3 } & 4\frac { 2 }{ 3 } & 7 \end{matrix}$

From this we can see that the second term is twice the first, the third is three times the first, or you could say, the $n^{th}$ term is $2\frac { 1 }{ 3 }\times n$ or, more simply, $\frac { 7n }{ 3 }$ .

Now, inputting the values $n=30$ and $n=60$ , we achieve:

$\frac { 7\times 30 }{ 3 }+\frac { 7\times 60 }{ 3 }$

Which, when simplifying the fraction, gives:

$7\times 10+7\times 20=70+140=\boxed {210}$

This means that the bakery were able to bake $70$ pies on the $30^{th}$ day and $140$ pies on the $60^{th}$ day, which gives a total of $210$ pies!