Chapter 11.2, Problem 22PPS

To determine

Write an equation for the nth term of the arithmetic sequence $a_9=45,d=-3$

Answer to Problem 22PPS

  $a_n=72-3n$

Explanation of Solution

Given:

The Information:$a_9=45,d=-3$

Concept Used:

The general equation for the nth term of arithmetic sequence is $a_n=a_1+(n-1)·d$

Given: The Information:$a_9=45,d=-3,\text{find}{a}_n$

Calculation:

Given: The Information:$a_9=45,d=-3,\text{find}{a}_n$

  $\begin{array}{l}{a}_9=45,d=-3,\text{find}{a}_1\\ a_n=a_1+(n-1)·d\\ a_9=a_1+(9-1)·-3\\ 45=a_1-24\\ 45+24=a_1-24+24\\ a_1=69\end{array}$

  $\begin{array}{l}{a}_1=69;d=-3,\text{find}{a}_n\\ a_n=a_1+(n-1)·d\\ a_n=69+(n-1)·-3=69-3n+3=72-3n\\ a_n=72-3n\end{array}$

Thus, the nth term of the sequence is $a_n=72-3n$