For each figure, how is the number on the center tile related to the numbers on the other tiles?What will the center number in Figure 6?What will the center number be in figure 10?

9-3Sequences and Series

Unit Objectives:• Write and use recursive definitions for a sequence.• Write and use explicit formulas for a sequence.• Determine if sequences are arithmetic or geometric.• Find values for sequences and series.

Today’s Objective:I can define, identify and apply arithmetic sequences.

Recursive Definition:Uses the previous term ()Two Parts: Initial Value

Recursive Rule

Explicit Formula:Describes sequenceusing term number (n)

Sequences

Sequence:Ordered list of numbers

Term of a Sequence:Each number: n represents term number

𝑎𝑛=¿ 𝑎1=¿𝑎𝑛=¿

2𝑎𝑛−1+2

2𝑛

1st Term 2nd Term 3rd Term … n – 1 term nth term n + 1 term …

↓ ↓ ↓ ↓ ↓ ↓, , , … , , , …

2, 4, 6, 8, …

Arithmetic Sequencea, a + d, a + 2d, a + 3d, …

a = starting valued = common difference

Recursive Definition:

for

Explicit Formula: for

4, 7, 10, 13, 16, …

+3 +3 +3 +3

Recursive Definition:4

+3𝑎𝑛−1

Explicit Formula: 4+(𝑛−1 )

1, 4, 9, 16, 25, …

3 5 7 9Not an Arithmetic Series

Find the 2nd and 3rd term of:100, ▒ , ▒, 82, …

Analyzing Arithmetic SequencesFind the 46th term:3, 5, 7, …

Explicit Formula:

3+ (46−1 )⋅2¿93𝑎46=¿−18=3𝑑−6=𝑑

82=100+3𝑑3+(𝑛−1 )𝑎𝑛=¿ 100¿+ (−1 )8 2

94, 88,

Find the 24th term: 4, 7, 10, …

4+ (24−1 ) ⋅3𝑎24=¿ ¿73Finding missing term:…, 15, ▒ , 59, …

Arithmetic Mean: 15+592

37,

The number of seats in the first 13 rows in a section of this arena form an arithmetic sequence.

How many seats are in row 13?

¿3814+(13−1 )𝑎13=¿

𝑎𝑛=𝑎(𝑛−1)⋅ 𝑑

Pg. 575 #9-60 by 3s