1. Arithmetic Series/Geometric Series Review

2. Sum of a Finite Arithmetic Series Where: S n is the sum of all the terms n = number of terms a 1 = first term a n = last term

3. Problem 1: Find the sum of the following series: 2, 11, 20, 29, 38, 47

4. Problem 2: A 20-row movie theatre has three sections of seating. In each section, the number of seats in a row increases by one with each successive row. The first row of the middle section has 10 seats. The front row of each of the two side sections has 4 seats. Find the total number of chairs in each section. Then find the overall total number of chairs.

5. Formula for the Sum of a Finite Geometric Series n = # of terms a 1 = 1 st term r = common ratio

6. Problem 1: Find the sum of the following series: 3, 6, 12, …. 96

7. Problem 2: In March, the Floyd family stars saving for a vacation at the end of August. The Floyds expect to the vacation to cost $1375. They start with $125. Each month they will deposit 20% more than the previous month. Will they have enough money for their trip?

8. Summation When we don’t want to write out a whole bunch of numbers in the series, the summation symbol is used when writing a series. The limits are the greatest and least values of n. Summation symbol Upper Limit (greatest value of n) Lower Limit (least value of n) Explicit function for the sequence So, the way this works is plug in n=1 to the equation and continue through n=3. (5*1 + 1) + (5*2 +1) + (5*3 + 1) = 33

9. Writing a series in summation form Ex: 102 + 104 + 106 + 108 + 110 + 112 n = 6 terms 1 st term = 1 Rule: Hmmmm.... Rule = 100 + 2n Let’s Evaluate: Yes, you can add manually. But let’s try using the shortcut:

10. Let’s try some Find the number of terms, the first term and the last term. Then evaluate the series:

11. Let’s try some Find the number of terms, the first term and the last term. Then evaluate the series: N = 10 1 st = 1 Last = 10 a 1 = 1-3 = -2 a 10 = 10-3 = 7 N = 4 1 st = 2 Last = 5 4+9+16+25 = 54 Notice we can use the shortcut here: Why is the answer not 58? Note: this is NOT an arithmetic series. You can NOT use the shortcut; you have to manually crunch out all the values.