Word Problem: Arithmetic Sequence

Question

A teaching position has a starting salary of $60,000 with a raise of $3000 every year thereafter.

a. Write an expression for the nth term of an arithmetic sequence that represents the salary as a function of the number of years of employment, n.

b. Find the total income for an employee who works at the job for 30 yrs.

Answer 1

Since we have arithmetic sequence, the common difference among the salaries is 3000.

 

S_n = 60000 + 3000(n - 1)

 

where:

S_n = salary

n = number of years of employment

 

 

To find the total income for 30 years, evaluate S₃₀.