Introduction to sequences
A:
- Ways to specify a sequence
- Finding of one or more members of a sequence
B:
- 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
Arithmetic sequences
A:
- Defining a sequence (nth term formula or recurrent relation)
- Finding the nth term of a sequence
- Finding the common difference of a sequence
B:
- 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
C:
- Word problems
- Equations and inequalities containing sums of sequences
Geometric sequences
A:
- Defining a sequence (nth term formula or recurrent relation)
- Finding the nth term of a sequence
- Finding the common ratio of a sequence
B:
- 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
C:
- Word problems
- Combinations of arithmetic and geometric sequences
Limit of a sequence
A:
- 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
B:
- Evaluation of limits with trigonometric, exponential and logarithmic functions
C:
- 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
A:
- Summation notation
- Finding of the first term and of the common ratio of a geometric sequence
- The sum of an infinite geometric series
B:
- Periodic numbers (repeating decimals)
- Finding of all x for which a series diverges or converges
- Solving equations with infinite series
- Word problems
