Question

Mia takes a job with a starting salary of $40,000 for the first year. She earns a 3% increase each year. Write an equation for the partial sum of the geometric sequence used to model the situation and explain what an, n, Sn, and r represent (use a_n to represent an).​

Answer 1

The partial sum that models the situation

is Sn=a1(1 - rn)/(1 - r).

n = number of years Mia works this job

an = Mia's salary during her nth year

Sn = total amount Mia earns after n years

r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase

Explanation:

Answer 2

The partial sum that models the situation

is Sn=a1(1 - rn)/(1 - r).

n = number of years Mia works this job

an = Mia's salary during her nth year

Sn = total amount Mia earns after n years

r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase