## Thinking Mathematically (6th Edition)

The number of students increasing geometrically is worse than the number of students increasing arithmetically. Example: Suppose first day only one student is affected. Now, suppose that$d=2$ for arithmetically increasing of affected students. The number of student affected after 30 days will be: \begin{align} & {{S}_{n}}=\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right] \\ & =\frac{30}{2}\left( 2+29\times 2 \right) \\ & =15\times 60 \\ & =900 \end{align} Let $r=2$ for geometric increase of number of affected students The number of student affected after 30 days will be: \begin{align} & {{S}_{n}}=\frac{a\left( {{r}^{n}}-1 \right)}{\left( r-1 \right)} \\ & {{S}_{n}}=\frac{1\left( {{2}^{30}}-1 \right)}{\left( 2-1 \right)} \\ & =\left( {{2}^{30}}-1 \right) \\ & {{S}_{n}}=1073741827 \end{align} If the number increases geometrically it is worse.