ARITHMETIC AND GEOMETRIC SEQUENCES
CHAPTER 1: REAL NUMBER SEQUENCES
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A. SEQUENCES
1. Definition
2. Criteria for the Existence of a Sequence
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B. TYPES OF SEQUENCE
1. Finite and Infinite Sequences
2. Monotone Sequences
3. Piecewise Sequences
4. Recursively Defined Sequences
–Activity: The Fibonacci Sequence and the Golden Ratio
–Activity: Polygonal Numbers
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CHAPTER 2: ARITHMETIC SEQUENCES
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A. ARITHMETIC SEQUENCES
1. Definition
2. General Term
3. Advanced General Term Formula 22
4. Middle Term Formula (Arithmetic Mean)
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B. SUM OF THE TERMS OF AN ARITHMETIC SEQUENCE
1. Sum of the First n Terms
2. Applied Problems
–Activity: Magic Squares
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CHAPTER 3: GEOMETRIC SEQUENCES
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A. GEOMETRIC SEQUENCES
1. Definition
2. General Term
3. Advanced General Term Formula
4. Common Ratio Formula
5. Middle Term Formula (Geometric Mean)
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B. SUM OF THE TERMS OF A GEOMETRIC SEQUENCE
1. Sum of the First n Terms
2. Applied Problems
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C. INFINITE SUM OF A GEOMETRIC SEQUENCE (OPTIONAL)
1. Infinite Sum Formula
2. Repeating Decimals
3. Equations with Infinitely Many Terms
4. Applied Problems
–Activity: The Sierpinski Pyramid
–Activity: The Koch Snowflake