# Unit 9 Mind Map Sequences and Series

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Unit 9 Mind Map Sequences and Series

## 1. Lesson 1

### 1.1. Arithmetic

1.1.1. An=A1+(n-1)(d)

1.1.2. D=A2-A1

1.1.4. Common difference

### 1.2. Geometric

1.2.1. Multiplication

1.2.2. Common ratio

1.2.3. r=A2 / A1

1.2.4. An=A1(r)^n-1

1.2.5. 2,12,72,432,2592

1.2.5.1. r=6

1.2.6. What is the 10th term of the geometric sequence with a first of 884 and a common ratio of 2.

1.2.6.1. 884(2)^10-1

## 2. Lesson 2

### 2.1. Sum of Arithmetic sequences

2.1.1. n/2 [2a1+ (n-1)d]

2.1.1.1. Sum15+15/2[2(5)+15-1)-20]

2.1.2. What is the sum of the first 20 arithmetic sequence shown?

2.1.3. d=common difference

2.1.4. Sum(n)=n/2 [2a1+ (n-1)d]

### 2.2. Sum of Geometric sequences

2.2.1. sum(n)= a1(1-r^n)/(1-r)

2.2.2. r≠1

2.2.3. Common ratio a2 / a1

2.2.4. What is the sum of the first 10 terms of the Geometric sequence

2.2.5. Sum10=5(1-5^10) / 1-5

2.2.5.1. Sum10=12270030

## 3. Lesson 3

### 3.1. Infinite Geometric Series

3.1.1. sum∞= a1/ 1-r

3.1.2. |r|<1

3.1.3. Find the sum of the infinite geometric

3.1.4. 3072+ 768+ 192+ 48

3.1.4.1. sum∞= 3072/ 1-0.25

3.1.4.1.1. sum∞=4096

### 3.2. Sigma Notation

3.2.1. Σ

3.2.1.1. Press Math, then 0: SummationΣ

3.2.1.1.1. Σ

3.2.2. ∞=999

3.2.3. ^Σ↓ x=1 (#)

3.2.4. ∞Σx=1 (1/3)^x-1