Video lecture (English) of C03 Sequences
C03 Sequences
对应大纲的内容
| M4.18 | Generate terms of a sequence using term-to-term or position-to-term rules. |
| M4.19 | Deduce expressions to calculate the $\boldsymbol{n}$th term of linear or quadratic sequences. |
| MM2.1 | Sequences, including those given by a formula for the $\boldsymbol{n}$th term and those generated by a simple recurrence relation of the form $\boldsymbol{x_{n+1} = f(x_{n})}$. |
学习目标
- Analyse recurrence relations by generating terms and tracing the iterative logic of $u_{n+1}$ $=$ $f\left(u_n\right)$ to predict global behaviour, such as convergence, divergence, or cyclic oscillation.
- Derive explicit position-to-term formulae $\left(u_n\right)$ for linear and quadratic sequences using first and second differences to bridge the gap between discrete sequences and continuous functions.
- Evaluate complex series sums $(\sum u_n)$ by identifying terms that systematically cancel out in telescoping series or by recognising periodic loops generated by cyclic recurrence relations.
- Solve advanced piecewise recursive sequences by tracking the terms logically when the recurrence rule alters based on the parity or modular properties of the index $n$.
- Synthesise discrete sequence logic with continuous calculus operations to evaluate iterative recurrence relations involving foundational differentiation rules, such as $f_{n+1}(x)=x f_n^{\prime}(x)$.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 11 | 90 min |
| Quiz | 7 | 30 min |
| Practice A | 25 | 45 min |
| Practice B | 20 | 50 min |
| Total | 63 | approx. 3-4 hrs |
