# Thread: Sequences - Job Offer Problem

1. ## Sequences - Job Offer Problem

Greetings,

This did not trip any key words. Any help?
Suppose you just received a job offer with a startingsalary of 37,000 per year and a guaranteed raise of 1500 per year. How manyyears will it take before you've made a total (or aggregate) salary of \$ 1,025,000?

2. ## Re: Sequences - Job Offer Problem

The salary sequence forms an arithmetic progression.
37000, 37000+1500, 37000+3000,..........
So the first term of the AP is a=37000 and the common difference is d=1500.
The number of years will be the number of terms of the sequence (n).
The total salary is 1,025,000.
So we have to find the number of terms of the sequence that will add upto give 1,025,000.
Sum to n terms of an AP is given by
Sn=n/2[2*a+(n-1)d]
where Sn=1,025,000
a=37000 and d=1500.
You will get a quadratic equation in n which has to be solved to find the required number of years.

3. ## Re: Sequences - Job Offer Problem

OK, I guess the instructor randomly changed the values and it made such difficult numbers to work with, I assumed we were on the wrong track. You don't normally give high school kids problems where completing the square yields factors to three decimal places. Ouch!