Chapter 9, Problem 20RE

To determine

To write:The terms of the given infinite sequence.

Explanation of Solution

Given: The sales of the lottery tick is modelled by,

  $a_n=-0.18n^2+37n+35$

The sales of the lottery tick is modelled by,

  $a_n=-0.18n^2+37n+35$ ...... (1)

Substitute $1$ for $n$ in equation (1)

  $\begin{array}{c}{a}_1=-0.18{\left(1\right)}^2+37\left(1\right)+35\\ =38.52\end{array}$

Substitute $2$ for $n$ in equation (1)

  $\begin{array}{c}{a}_2=-0.18{\left(2\right)}^2+37\left(2\right)+35\\ =41.68\end{array}$

Substitute $3$ for $n$ in equation (1)

  $\begin{array}{c}{a}_3=-0.18{\left(3\right)}^2+37\left(3\right)+35\\ =44.68\end{array}$

Substitute $4$ for $n$ in equation (1)

  $\begin{array}{c}{a}_4=-0.18{\left(4\right)}^2+37\left(4\right)+35\\ =46.92\end{array}$

Substitute $5$ for $n$ in equation (1)

  $\begin{array}{c}{a}_5=-0.18{\left(5\right)}^2+37\left(5\right)+35\\ =49.00\end{array}$

Substitute $6$ for $n$ in equation (1)

  $\begin{array}{c}{a}_6=-0.18{\left(6\right)}^2+37\left(6\right)+35\\ =50.72\end{array}$

Substitute $7$ for $n$ in equation (1)

  $\begin{array}{c}{a}_7=-0.18{\left(7\right)}^2+37\left(7\right)+35\\ =52.08\end{array}$

Substitute $8$ for $n$ in equation (1)

  $\begin{array}{c}{a}_8=-0.18{\left(8\right)}^2+37\left(8\right)+35\\ =53.08\end{array}$

Substitute $9$ for $n$ in equation (1)

  $\begin{array}{c}{a}_9=-0.18{\left(9\right)}^2+37\left(9\right)+35\\ =53.72\end{array}$

Substitute $10$ for $n$ in equation (1)

  $\begin{array}{c}{a}_{10}=-0.18{\left(10\right)}^2+37\left(10\right)+35\\ =54.00\end{array}$

The graph is plotted below.

  

Figure (1)