Study Notes
Sequences in algebra involve patterns of numbers that follow specific rules. Geometric Sequence — a sequence where each term is obtained by multiplying the previous term by a constant, known as the common ratio. Example: In the sequence 2, 6, 18, 54, the common ratio is 3. Arithmetic Sequence — a sequence where each term is obtained by adding a constant to the previous term. Example: In the sequence 6, 10, 14, 18, the common difference is 4. Quadratic Sequence — a sequence where the second difference between terms is constant. Example: In the sequence 2, 7, 14, 23, the second difference is 2. Cubic Sequence — a sequence where the third difference between terms is constant. Example: In the sequence 4, 16, 44, 94, the third difference is 6.
Exam Tips
Key Definitions to Remember
- Geometric Sequence: A sequence where each term is found by multiplying the previous term by a constant.
- Arithmetic Sequence: A sequence where each term is found by adding a constant to the previous term.
- Quadratic Sequence: A sequence with a constant second difference.
- Cubic Sequence: A sequence with a constant third difference.
Common Confusions
- Mixing up the common ratio with the common difference.
- Forgetting to use n-1 in the formula for the nth term of a geometric sequence.
Typical Exam Questions
- What is the 1,000th term in the sequence 3, 7, 11,...? Use the formula for arithmetic sequences to find the term.
- What is the 10th term in the sequence with nth term 3n−10? Substitute n=10 into the formula to find the term.
- Find the nth term of the sequence 4, 16, 44, 94, 172, 284. Use the method for finding the general term of a cubic sequence.
What Examiners Usually Test
- Ability to identify the type of sequence from given terms.
- Calculating the nth term using the appropriate formula.
- Solving problems involving the sum of terms in a sequence.