Chapter 8.2, Problem 40E

To determine

To calculate: The rule for the sequence with the given terms.

Answer to Problem 40E

The rule is $a_n=-5n+20$ .

Explanation of Solution

Given information:

  .

Formula used:

Arithmetic difference − the difference of consecutive term is constant. The constant difference is called the common difference and is denoted by d .

Therefore,

  $d=a_{n+1}-a_n;n\ge 1$ .

The $nth$ tem of an arithmetic sequence with first term $a_1$ and common difference $d$ is given by : $a_n=a_1+(n-1)d$ .

Calculation:

Consider the points in table form,

$n$	$1$	$2$	$3$	$4$
$a_n$	$15$	$10$	$5$	$0$

  $\begin{array}{l}{a}_1=15\\ a_2=10\\ a_3=5\\ a_4=0\\ d=a_2-a_1\\ =10-15\\ =-5\end{array}$

The general rule.

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ =15+(n-1)(-5)\\ =15-5n+5\\ =-5n+20\end{array}$

Hence, the rule for the sequence is $a_n=-5n+20$ .