Question

Use the following information. At the start of your second year as a veterinary technician, you receive a raise of \(\$750.\) You expect to receive the same raise every year. Your total yearly salary after your first raise is \(\$ 18,000\) per year. Calculate your yearly salary after six years as a veterinary technician.

Short answer

The yearly salary after six years as a veterinary technician will be \$21,750.

Step-by-step solution

Identify the first term, common difference, and number of terms

Web start by identifying the components of the arithmetic progression. The first term \(a\) (i.e., the salary in the second year) is \$18,000, the common difference \(d\) (i.e., the annual raise) is \$750, and the number of terms \(n\) is six (i.e., the years worked).

Apply the arithmetic progression formula

Next, we apply the arithmetic progression formula to calculate the 6th term in the progression. The nth term of an arithmetic progression can be found using the formula \(a_n = a + (n-1) * d\).

Calculate the yearly salary after six years

We substitute the given values into the formula to calculate the 6th term of the progression, which corresponds to the yearly salary after six years. Therefore, \(a_6 = 18000 + (6 - 1) * 750 = 18000 + 3750 = \$21750\).