Chapter 8.2, Problem 43E

To determine

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

Answer to Problem 43E

The rule is $a_n=4n+21$ .

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 table ,

$n$	$4$	$5$	$6$	$7$	$8$
$a_n$	$25$	$29$	$33$	$37$	$41$

  $\begin{array}{l}{a}_4=25\\ a_5=29\\ a_6=33\\ a_7=37\\ d=a_5-a_4\\ =29-25\\ =4\end{array}$

The general rule.

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ =25+(n-1)(4)\\ =25+4n-4\\ =4n+21\end{array}$

Hence, the rule for the sequence is $a_n=4n+21$ .