Chapter MPS, Problem 11.2MPS

a.

To determine

Money earned by Mr. Patton in the last year.

Answer to Problem 11.2MPS

Mr. Patton will make $ $74000$ in his last year.

Explanation of Solution

Given information:

Starting salary of Mr. Patton = $40000

The hike in Mr. Patton salary every year = $1000

Mr. Patton retires after 35 years.

Formula used:

Nth term of arithmetic sequence:

  $a_n=a+\left(n-1\right)d$

  a = First term of the series.

  d = Common difference

  n= Number of terms

  $a_n$ = nth term

As we know the income Mr. Patton in increasing by $1000 every year, therefore the common difference(d) will be 1000 i.e. $d=1000$

As the starting salary of Mr. Patton is $40000, therefore $a=40000$

Now finding Mr. Patton salary in his last year or after 35 years by using formula $a_n=a+\left(n-1\right)d$ :

Here $a=40000,d=1000,n=35$

  $\begin{array}{l}{a}_{35}=40000+\left(35-1\right)1000\\ a_{35}=40000+\left(34\right)1000\\ a_{35}=40000+34000\\ \boxed{a_{35}=74000}\end{array}$

Mr. Patton salary in his last year will be $ $74000$ .