1. LT: I can evaluate Arithmetic and Geometric Series.
Warm-Up

2. Arithmetic and Geometric Series
LT: I can evaluate Arithmetic and Geometric Series.
Arithmetic and Geometric Series

3. LT: I can evaluate Arithmetic and Geometric Series.
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 - …

4. Finite Arithmetic Series
LT: I can evaluate Arithmetic and Geometric 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

5. Example n = 60 a1 = 9 a60 = ? a60 = 9 + (60 – 1)5 = 304
LT: I can evaluate Arithmetic and Geometric Series.
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

6. Finite Geometric Series
LT: I can evaluate Arithmetic and Geometric Series.
WARNING: you MUST have a Geometric Series to use this formula an = a1 * r (n-1)

7. LT: I can evaluate Arithmetic and Geometric Series.
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

8. Another Way to Write it…
LT: I can evaluate Arithmetic and Geometric Series.
Another Way to Write it…

9. But what if our series doesn’t start at 1?
LT: I can evaluate Arithmetic and Geometric Series.
But what if our series doesn’t start at 1?
This would be done the same way for geometric series, but with the geometric formula

10. LT: I can evaluate Arithmetic and Geometric Series.
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

11. LT: I can evaluate Arithmetic and Geometric Series.
Closure