Arithmetic Series:

A child's mother gives her 10 cents one day. Everyday thereafter her mother gives 3 more cents than the previous day. After 20 days how much does she have?
Solution:
The list of the amounts she gets each day can be written as arithmetic sequence as:
10, 13, 16, 19, 22..............
When we add up we get the series:
10 + 13 + 16 + 19 + 22 + ...................
Here a = 10, d = 3 and n = 20
The sum = n/2 (2a + (n1)d )
= 20/2 (1(10) + 19(3) )
= 10 (77)
= 770
Answer: 770 cents

An auditorium has 20 rows of seats. There are 20 seats in the first row., 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows?
Solution:
The number of seats in the 20 rows form an arithmetic sequence in which the common difference is d = 1
nth term = a_{20} = a_{1} + (n1)d
= 20 + 19(1)
= 20 + 19
= 39
Sum of 20 terms is:
S^{n} = n/2 (a_{1} + a_{20})
= 20/2 (20 + 39)
= 10 (59)
= 590
Answer: 590

Suppose that you play black jack at Harri's on June 1 and lose $1,000. Tomorrow you bet and lose $15 less. Each day you lose $15 less that your previous loss. What will your total losses be for the 30 days of June?
Solution
This is an arithmetic series with a^{1} = 1000 and d = 15
We can calculate
a30 = 1000  15(30  1) = 565
Now we use the formula
S30 = 30/2 (1000 + 565) = 23,475
You will lose a total of $23,475 during June.
Answer: $23,475

John works for a company and gets a starting salary of $32,500 and annual raise of $1500.
Determine the persons salary during the sixth year of employment and the total compensation from the company through 6 full years of employment.
Answer: $40,000 and $217,500
Directions: Answer the following questions. Also write at least 5 examples of your own.
