Arithmetic Series?

Question

The first-year salary of an employee is $34,500. Each year thereafter, her annual salary increases by $750.

a. What will her salary be during her tenth year of work?

b. What will her total earnings be for 25 years of work?

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Answer 1 · 2018-04-22T14:42:43

See below

I can model the employees, salary with:
#a_n=a_1+d(n-1)#

#a_n# is the nth term
#a_1# is the first term
#d# is the difference

So:
#a_n= 34500+750(n-1)#

a. So for the tenth year:
#a_10= 34500+750(10-1)=41,250# dollars

Her total earnings after 25 years of work:
#S_n= n/2(a_1+a_n)#

Where #n# is 25
#a_25= 34500+750(25-1)=52,500# dollars

#S_25= 25/2(34500+52500)= 1,087,500# dollars