1. Arithmetic and Geometric Series

2. Sequence vs. Series
Sequence – a set of numbers that follow a general rule Examples: 1, 8, 15, 22, 29, …
-8, 2, -1/2, 1/8, …
Series – the sum of the terms in a sequence of numbers
Examples: …
– 1/2 + 1/8 - …

3. Finite Arithmetic Series
WARNING: you MUST have an Arithmetic Series to use this formula
Reminder: the formula for an arithmetic sequence is an = a1 + (n – 1)d

4. Example n = 60 a1 = 9 a60 = ? a60 = 9 + (60 – 1)5 = 304
Find the sum of the first 60 terms in the arithmetic series 9, 14, 19, …
n = a1 = a60 = ?
an = a1 + (n – 1)d
a60 = 9 + (60 – 1)5
= 304
S60 = 60 ( ) 2
= 30 (313)
= 9390

5. Finite Geometric Series
WARNING: you MUST have a Geometric Series to use this formula an = a1 * r (n-1)

6. Example Sn = a1 (1 – rn) – r
Find the sum of the first ten terms of the geometric series
16, – 48, 144, – 432,…
n = 10 a1 = 16 r = -3
S10 = 16 [1 – (-3)10]
1 – (-3)
= 16 (1 – 59,049) 4
= -236,192

7. Another Way to Write it…

8. But what if our series doesn’t start at 1?
3rd 3 3 16 3 16 48
212
212 24 48
This would be done the same way for geometric series, but with the geometric formula

9. Things to remember
A sequence is a list of numbers, a series is a sum of that list of numbers
You need to know the formulas for arithmetic and geometric sequences and for arithmetic and geometric series (4 formulas)
If your series doesn’t start at 1 then you must create a subtraction problem to find the series

10. Make sure you took notes, did all examples, and answer the questions on the website