Question

An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically.

Answer 1

Offer B canbe represented by an arithmetic sequence because there is a constant difference between the salary of two consecutive years.

The sequence can be written as follow:

Bn = 56,000 + 3,000n

where n is the number of years in the job.

By subtracting B(n+1) - Bn, you obtain:

$\begin{gathered} B_{n+1}-B_n=56,000+3,000(n+1)-56,000-3,000n \\ B_{n+1}-B_n=3,000 \end{gathered}$

As you can notice, the difference of the salaries between two consecutive years is constant, which means that Bn is an arithmetic sequence.