1. Prepares for A-SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

2. Sequence
Term of a Sequence
Explicit formula
Recursive formula

3. Paper for notes
Pearson 9.1
Calculator

4. TOPIC:
Mathematical Patterns
Name: Daisy Basset Date :
Period: Subject:
Notes
Objective:
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

5. Vocabulary Sequence Term of a Sequence Explicit Formula
Recursive Formula

6. A sequence has an explicit formula an = 3n - 2
A sequence has an explicit formula an = 3n What are the first 5 terms of this sequence?

7. n
an = 3n -2 1 2 3 4 5
a1 = 3(1) – 2 = 1
a2 = 3(2) – 2 = 4
a3 = 3(3) – 2 = 7 10
a4 = 3(4) – 2 =
a5 = 3(5) – 2 = 13

8. 2. A sequence has an explicit formula an = 10n + 4
2. A sequence has an explicit formula an = 10n What is term a12 in the sequence?

9. an = 10n + 4
a12 = 10(12) + 4
a12 = 124

10. 3. What is a recursive definition for the sequence?

11. A. -2, 0, 2, 4, …
Subtract consecutive terms to find out what happens from one term to the next.

12. a2 – a1
a3 – a2
a4 – a3
0 – -2 = 2
2 – 0 = 2
4 – 2 = 2
an – an-1 = 2

13. a1 = -2 an – an-1 = 2 + an-1 + an-1 and a1 = -2 an = an-1 + 2
To write a recursive definition, state the initial condition and the recursive formula.
a1 = -2
an – an-1 = 2
+ an an-1
and
a1 = -2
an = an-1 + 2

14. B. 4, -8, 16, -32, 64, …
Subtract consecutive terms to find out what happens from one term to the next.

15. an = -2 an-1 a2 – a1 a3 – a2 a4 – a3 a5 – a4 -8 – 4 = 16 – -8 = 24
-12 -2
16 – -8 = 24 -2
-32 – 16 =
-48 -2
64 – -32 = 96 an = -2
an-1

16. an a1 = 4 = an-1 -2 1 a1 = 4 and an = -2(an-1)
To write a recursive definition, state the initial condition and the recursive formula. an -2
a1 = 4 =
an-1 1
a1 = 4
and
an = -2(an-1)

17. Summary
Summarize/reflect  D
 What did I do? L 
 What did I learn?  I
 What did I find most interesting? Q 
 What questions do I still have? What do I need clarified?