Higher Maths
Sequences Checklist
Covering every mandatory skill for Recurrence Relations. Use the Clelland Maths Masterclass video to master these Paper 1 and Paper 2 techniques.
1
Building & Stepping
Calculate Terms
Apply \( u_{n+1} = au_n + b \) to find future terms like \( u_2 \) or \( u_4 \).
Backward Iteration
Rearrange to find a previous term (e.g., finding \( u_0 \) from \( u_1 \)).
Identify Initial Values
Distinguish between "initial" (\( u_0 \)) and "term 1" (\( u_1 \)).
2
Limit Theory
The Existence Mark
State that a limit exists because \( -1 < a < 1 \).
Calculate Limit (L)
Use the formula \( L = \frac{b}{1-a} \) or solve \( L = aL + b \).
3
Modelling in Context
Write Relations from Text
Convert growth/decay narratives into an equation (e.g., declining population).
Long-term Stabilization
Interpret the limit as a steady state in real-life situations.
4
Advanced Algebra
Simultaneous Equations
Calculate unknown \( a \) and \( b \) from three terms (i.e \( u_0 \), \( u_1 \) and \( u_2 \)).
Convergence Range
Find values of \( k \) for which a sequence converges.
Quadratic Inequalities
Solve quadratics (e.g., \( k^2 \dots \)) to find the range of values for a limit or specific condition.
🎓
SQA Exam Tips
- The Limit Existence mark requires you to explicitly state \( -1 < a < 1 \).
- Always provide a concluding statement relating your limit back to the context.
- For non-calculator Paper 1, keep multipliers as exact fractions (e.g., \( \frac{1}{5} \)).