# Sequences and series

The topic is divided into the following subtopics:
• Introduction to sequences
• Arithmetic sequences
• Geometric sequences
• Limit of a sequence
• Infinite series

### Introduction to sequences

Part I:
• Ways to specify a sequence
• Finding of one or more members of a sequence
Part II:
• Defining a sequence (nth term formula or recurrent relation)
• Properties of sequences (strictly increasing or strictly decreasing, nonincreasing, nondecreasing, upper or lower bounded, bounded)
• Finding the nth term of a sequence
Part III:
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### Arithmetic sequences

Part I:
• Defining a sequence (nth term formula or recurrent relation)
• Finding the nth term of a sequence
• Finding the common difference of a sequence
Part II:
• Finding the nth term of a sequence – complex problems
• Finding the common difference of a sequence – complex problems
• Sum of the first n terms of a sequence
• Systems of equations containing sequence terms
Part III:
• Word problems
• Equations and inequalities containing sums of sequences

### Geometric sequences

Part I:
• Defining a sequence (nth term formula or recurrent relation)
• Finding the nth term of a sequence
• Finding the common ratio of a sequence
Part II:
• Finding the nth term of a sequence – complex problems
• Finding the common ratio of a sequence – complex problems
• Sum of the first n terms of a sequence
• Systems of equations containing sequence terms
Part III:
• Word problems
• Combinations of arithmetic and geometric sequences

### Limit of a sequence

Part I:
• Evaluation of limits of sequences containing polynomials and rational expressions
• Limit laws – sum of limits, difference of limits, product of limits and ratio of limits laws
Part II:
• Evaluation of limits with trigonometric, exponential and logarithmic functions
Part III:
• Use of the limit of the sequence (1+1/n)^n
• Evaluation of limits with radicals
• Evaluation of limits containing sums of sequences

### Infinite series

Part I:
• Summation notation
• Finding of the first term and of the common ratio of a geometric sequence
• The sum of an infinite geometric series
Part II:
• Periodic numbers (repeating decimals)
• Finding of all x for which a series diverges or converges
• Solving equations with infinite series
• Word problems
Part III:
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