Study Notes
Sequences and series involve lists of numbers and their sums. A sequence is an infinite list of numbers, often defined as a function from whole numbers to real numbers. Example: 7, 13, 19, 25, 31,...
- Arithmetic Sequence — a sequence where each term increases by a constant amount. Example: 3, 7, 11, 15,...
- Geometric Sequence — a sequence where each term is multiplied by a constant ratio. Example: 90, -30, 10, -3.33,...
- Series — the sum of terms of a sequence. Example: Sum of the first 20 terms of 3, 6, 12, 24,...
Exam Tips
Key Definitions to Remember
- A sequence is an infinite list of numbers.
- An arithmetic sequence increases by a constant difference.
- A geometric sequence multiplies by a constant ratio.
- A series is the sum of terms of a sequence.
Common Confusions
- Mixing up arithmetic and geometric sequences.
- Forgetting to apply the formula for the nth term correctly.
Typical Exam Questions
- What is the 50th term of the sequence 7, 13, 19,...? Use the formula for the nth term of an arithmetic sequence.
- Find the sum of the first 20 terms of the sequence 3, 6, 12,...? Use the formula for the sum of a geometric series.
- What is the common ratio of the sequence 90, -30, 10,...? Divide the second term by the first term.
What Examiners Usually Test
- Understanding and application of sequence formulas.
- Ability to find specific terms in sequences.
- Calculating sums of series using appropriate formulas.