Sequences

Summary and Exam Tips for Sequences

Sequences is a subtopic of Number, which falls under the subject Mathematics in the IB MYP curriculum. Sequences are ordered lists of numbers following specific patterns. In a Linear Sequence, the difference between consecutive terms is constant. For example, in the sequence 6, 10, 14, 18, the first difference is +4, leading to the general term $U_n = 4n - 2$. A Quadratic Sequence involves a second difference that is constant. For instance, in the sequence 2, 7, 14, 23, 34, the second difference is 2, resulting in the general term $U_n = n^2 + 2n - 1$.

Triangular Number Sequences are formed by arranging dots into triangles, with the formula $x_n = \frac{n(n+1)}{2}$. For example, the 60th triangular number is 1830. The Fibonacci Sequence is a series where each number is the sum of the two preceding ones, starting from 0 and 1. This sequence is represented by the rule $x_n = x_{n-1} + x_{n-2}$. The Fibonacci sequence is notable for its appearance in natural spirals.

Exam Tips

• Understand the Difference Method: For linear sequences, calculate the first difference to find the general term. For quadratic sequences, calculate both first and second differences.
• Memorize Key Formulas: Be familiar with the formulas for triangular numbers $x_n = \frac{n(n+1)}{2}$ and the Fibonacci sequence $x_n = x_{n-1} + x_{n-2}$.
• Practice Problem Solving: Work through examples to solidify your understanding of how to derive terms and solve equations for sequences.
• Check Your Work: Always verify your calculations, especially when solving simultaneous equations for quadratic sequences.
• Visualize Patterns: Use diagrams or drawings to better understand sequences like triangular numbers and Fibonacci spirals.