Respuesta :
Answer:
Step-by-step explanation:
From the question, we can form an equation like: S = 7200 + 350X
where S is the salary and X is year.
1. His salary in the 9th year, means X=9, so we substitute 9 into the equation to find S = 7200 +350 (9) = 10350
2. The total he will have in the first 12years, we have:
Sum of first n terms of an AP: S =(n/2)[2a + (n- 1)d] where a is the value of the 1st term, here a is 7200 and d = 350 the common difference between terms
=> S = (12/2)[2*7200 + (12- 1)350] = 109500
The salaries received form an arithmetic progression, A.P., and the salaries received with time can be determined using the formula for an A.P.
- The salary of the man in the 9th year is $10,000
- The total he will have in the first 12 years is $109,500
Reasons:
The annual salary at the commencement of employment = $7,200
The annual increment received = $350
Required:
The salary in the 9th year
Solution:
The annual salary that has an increase of $350 each year forms an arithmetic series, that has a general form of tₙ = a + (n - 1)·d
Where;
The first term, a = 7,200
n = The number years
d = The common difference = 350
In the 9th year, n = 9, which gives;
In the 9th year, t₉ = 7,200 + (9 - 1) × 350 = 10,000
- His salary in the 9th year = $10,000
Required:
The total he will have in the first 12 years
Solution:
The total amount is given by the formula for the sum, Sₙ of an arithmetic progression as follows;
- [tex]\displaystyle S_n = \mathbf{\frac{n}{2} \cdot \left[2 \cdot a +(n - 1) \cdot d \right]}[/tex]
Therefore, in the 12th year (n = 12), we have;
[tex]\displaystyle S_n = \frac{12}{2} \times\left[2 \times 7,200 +(12 - 1) \times 350 \right] = 109,500[/tex]
- The total amount he will have in the first 12 years = $109,500
Learn more about arithmetic progression here:
https://brainly.com/question/12054811
