You recently have been offered a job that pays you a monthly salary of $3500 and guarantees you a monthly raise of $180 during your first year on the job.

Question

1. Find the general term of this arithmetic sequence.
2. What will your monthly salary be at the end of your first year of work?

Answer 1

Remember that the general formula for an arithmetic sequence is: a_n = a₁ + (n - 1)d, where a_n is the general term, a₁ is your first term, n is the number of terms and d is the common difference.

In your problem, $3500 is the amount that you get in your first month, so that's your a₁. The monthly raise amount is $180, so that's the common difference (d). Finally, the one thing that's important to notice is that "n" is the number of months that has passed since starting the job (not the number of years).

#1: Find the general term of this arithmetic sequence.

Let's just substitute all of the values we just identified into the formula.

a_n = a₁ + (n - 1)d

a_n = 3500 + (n - 1)(180)

a_n = 3500 + 180n - 180

a_n = 3320 + 180n

#2: What will your monthly salary be at the end of your first year of work?

At the end of your first year of work, 12 months would have passed, so n = 12.

Let's substitute that into the equation for the general term that we found above.

a_n = 3320 + 180(12) = 5,480

Your monthly salary will be $5480.