Chapter 11.2, Problem 32WE

To determine

To calculate:

The value of $n$ for the following arithmetic sequence:

  $40,37,34,\mathrm{...}-29,\mathrm{...}$

Answer to Problem 32WE

The value of $n$ is $24$

Explanation of Solution

Given information:

  $40,37,34,\mathrm{...}-29,\mathrm{...}$

Calculation:

Know that:

  $\begin{array}{l}{a}_1=40\\ a_n=-29\end{array}$

The common ratio between each term is calculated as:

  $\begin{array}{l}d=37-40=-3\\ d=34-37=-3\end{array}$

Now, the number of the terms in the given sequence is calculated as:

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ -29=40+\left(n-1\right)\left(-3\right)\\ -69=-3n+3\\ 3n=72\\ n=24\end{array}$