Salary Increases: A man gets a job of $30000 a year. He promised $2300 raise each subsequent year. Find his total earnings for a 10-year period.
To find the total earnings for a 10-year period, we need to calculate the salary for each year and then sum them up.
The man starts with a salary of $30,000.
In the second year, he gets a $2,300 raise, so his salary becomes $30,000 + $2,300 = $32,300.
In the third year, his salary increases by another $2,300, so it becomes $32,300 + $2,300 = $34,600.
We can observe that the salary increases by $2,300 each year. This is an arithmetic sequence with a common difference of $2,300.
To find the salary for a given year, we can use the following formula:
Salary = Initial Salary + (Year - 1) * Common Difference
Let's calculate the salary for each year from the 4th year to the 10th year:
4th year: $34,600 + ($4 - 1) * $2,300 = $34,600 + $6,900 = $41,500
5th year: $41,500 + ($5 - 1) * $2,300 = $41,500 + $9,200 = $50,700
6th year: $50,700 + ($6 - 1) * $2,300 = $50,700 + $11,500 = $62,200
7th year: $62,200 + ($7 - 1) * $2,300 = $62,200 + $13,800 = $76,000
8th year: $76,000 + ($8 - 1) * $2,300 = $76,000 + $16,100 = $92,100
9th year: $92,100 + ($9 - 1) * $2,300 = $92,100 + $18,400 = $110,500
10th year: $110,500 + ($10 - 1) * $2,300 = $110,500 + $20,700 = $131,200
Now, let's sum up the salaries for the 10-year period:
Total earnings = $30,000 + $32,300 + $34,600 + $41,500 + $50,700 + $62,200 + $76,000 + $92,100 + $110,500 + $131,200 = $641,200
Therefore, the man's total earnings for a 10-year period would be $641,200.
To find the man's total earnings for a 10-year period, we can use the formula for the sum of an arithmetic series.
The first term (a) is $30,000, and the common difference (d) is $2,300.
The formula to find the sum of an arithmetic series is:
Sn = (n/2) * (2a + (n-1)d),
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Let's substitute the given values into the formula:
Sn = (10/2) * (2 * $30,000 + (10 - 1) * $2,300)
Simplifying the equation:
Sn = (5) * (2 * $30,000 + 9 * $2,300)
Sn = 5 * (60,000 + 20,700)
Sn = 5 * $80,700
Sn = $403,500
So, the man's total earnings for a 10-year period would be $403,500.
so you have an arithmetic series with
a = 30,000 , d = 2300
sum(10) = (10/2)(60000 + 9(2300) )
= 403,500