Chapter 9.2, Problem 69E

a.

To determine

the salary during the sixth year of employment.

Answer to Problem 69E

  $\$40,000$

Explanation of Solution

Concept Used:

The n^th term of an arithmetic sequence with first term $a_1$ and common difference d is given by:

  $a_n=a_1+\left(n-1\right)d$

Given problem represents an arithmetic sequence with first term $a_1=\$32,500$ and $d=\$1500$ .

Now the n^th term of this sequence is given by,

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =32500+\left(n-1\right)\left(1500\right)\\ =32500+1500n-1500\\ =31000+1500n\end{array}$

The salary during the sixth year of employment is the sixth term of this sequence.

  $\begin{array}{c}{a}_6=31000+1500\left(6\right)\\ =31000+9000\\ =40,000\end{array}$

Conclusion:

The salary during the sixth year of employment is$40,000.

b.

To determine

the total compensation from the company through six full years of employment.

Answer to Problem 69E

  $\$217,500$

Explanation of Solution

Concept Used:

The sum of first n terms of an arithmetic sequence with first term $a_1$ and last term $a_n$ is given by:

  $S_n=\frac{n}{2}\left(a_1+a_n\right)$

Given problem represents an arithmetic sequence with first term $a_1=\$32,500$ and $d=\$1500$ .

The total compensation from the company through six full years of employment is the sum of first 6 terms of this sequence which is given by:

  $\begin{array}{c}{S}_6=\frac{6}{2}\left(a_1+a_6\right)\\ =3\left(32,500+40,000\right)\\ =3\left(72,500\right)\\ =217,500\end{array}$

Conclusion:

The total compensation from the company through six full years of employment is $\$217,500$ .