Final answer:
The salary during the fifth year will be $51,600. The total compensation through five full years of employment will be $238,500. This problem is solved using the concept of an arithmetic sequence.
Step-by-step explanation:
The student is asking about the salary increment problem which can be solved using basic arithmetic sequences, a topic in mathematics. The starting salary for the job is $43,800, with an annual increase of $1,950.
Salary During the Fifth Year
To calculate the salary during the fifth year, we consider the yearly increase as a constant and add it to the starting salary for each of the first four years:
Salary in 5th year = Starting salary + 4 * Annual increase
Salary in 5th year = $43,800 + 4 * $1,950
Salary in 5th year = $43,800 + $7,800
Salary in 5th year = $51,600
Total Compensation Through Five Full Years
The total compensation over five years is the sum of the salaries for each year. This forms an arithmetic sequence where:
- First term (a) = $43,800(the starting salary)
- Common difference (d) = $1,950(the annual increase)
- Number of terms (n) = 5
The formula for the sum of the first n terms of an arithmetic sequence is given by:
S_n = n/2 * [2a + (n-1)d]
Total compensation for 5 years (S_5) = 5/2 * [2*$43,800 + (5-1)*$1,950]
Total compensation for 5 years (S_5) = 5/2 * [$87,600 + $7,800]
Total compensation for 5 years (S_5) = 5/2 * $95,400
Total compensation for 5 years (S_5) = $238,500