Chapter 11.5, Problem 32E

To determine

To calculate:

Rule for $n^{th}$ term and identify type of sequence.

Answer to Problem 32E

Given is arithmetic sequence and Rule for $n^{th}$ term is $d=20-3n$ .

Explanation of Solution

Given information:

  

Calculation:

Given pairs are,

  $\begin{array}{l}\left(1,17\right)\\ \left(2,14\right)\\ \left(3,11\right)\\ \left(4,8\right)\end{array}$

Lets note the sequence by $a_w$ ,

  $\begin{array}{l}{a}_1=17\\ a_2=14\\ a_3=11\\ a_4=8\end{array}$

Also it is note that,

  $a_2-a_1=a_3-a_2=a_4-a_3=-3$

As the difference between consecutive terms is constant $a_n$ is an arithmetic sequence,having the elements.

  $\begin{array}{l}{a}_1=17\\ d=-3\end{array}$

Rule for $n^{th}$ term is,

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ d=1+\left(n-1\right)\left(-3\right)\\ d=17-3\left(n-1\right)\\ d=17-3n+3\\ d=20-3n\end{array}$

Hence, given is arithmetic sequence and Rule for $n^{th}$ term is $d=20-3n$ .