Sequences

Summary and Exam Tips for Sequences

Sequences is a subtopic of Numbers, which falls under the subject Mathematics in the IB MYP curriculum. In sequences, we explore various types of number patterns, including Linear Sequences, Quadratic Sequences, Triangular Number Sequences, and the Fibonacci Sequence.

• Linear Sequences: These sequences have a constant difference between consecutive terms. The general term is expressed as $U_n = an + b$. For example, in the sequence 6, 10, 14, 18, the first difference is +4, leading to $a = 4$ and $b = -2$, giving the nth term as $U_n = 4n - 2$.

• Quadratic Sequences: These sequences have a constant second difference. The general term is $U_n = an^2 + bn + c$. For the sequence 2, 7, 14, 23, 34, the second difference is 2, indicating $a = 1$. Solving simultaneous equations gives $b = 2$ and $c = -1$, resulting in $U_n = n^2 + 2n - 1$.

• Triangular Number Sequences: These sequences are formed by arranging dots in a triangular pattern. The formula for the nth triangular number is $x_n = \frac{n(n+1)}{2}$.

• Fibonacci Sequence: This sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones. The rule is $x_n = x_{n-1} + x_{n-2}$.

Exam Tips

• Understand the Difference Method: For both linear and quadratic sequences, mastering the difference method is crucial. Practice calculating first and second differences to find the general term.

• Memorize Key Formulas: Ensure you remember the formulas for triangular numbers and the Fibonacci sequence. These are often tested in exams.

• Practice Problem Solving: Work on example problems to solidify your understanding. Use the given sequences to practice deriving the nth term.

• Check Your Work: Always verify your solutions by substituting back into the sequence to ensure accuracy.

• Use Visual Aids: For triangular and Fibonacci sequences, drawing diagrams can help visualize and understand the patterns better.