The salary scale for a senior officer starts at N57000
per annum. A rise of N2800 is given at the end of each
Find the total amount of money that the officer will
year.
earn in 14 years.​

Respuesta :

Answer:

N1,052,800.

Step-by-step explanation:

The starting salary of the officer = N57,000

Increase per annum =N2,800

The given pattern forms an arithmetic sequence since the annual salary increases by a fixed amount.

We are to determine the total amount of money that the officer will earn in 14 years.​

Sum of an arithmetic sequence, [tex]S_n=\frac{n}{2}[2a+(n-1)d]$ ,where: \left\{\begin{array}{lll}$First term, a=57,000\\$Common difference, d=2,800\\$Number of terms, n=14\end{array}\right[/tex]

[tex]S_{14}=\frac{14}{2}[2(57,000)+(14-1)(2,800)]\\=7[114,000+13*2800]\\=7[150,400]\\=1,052,800[/tex]

At the end of 14 years, the total amount earned by the officer will be N1,052,800.