Learning objective
D2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n); work with increasing, decreasing and periodic sequences.
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Topic
Pure Mathematics
Subtopic
Sequences
Aqa A Level MathematicsPaper 1
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Quick explanation
D2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n); work with increasing, decreasing and periodic sequences
- This point belongs to Pure Mathematics, especially Sequences.
- You need to be able to d2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n); work with increasing, decreasing and periodic sequences.
- The key ideas to know are decreasing, periodic, and increasing.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Key concepts
decreasingperiodicincreasingnth termsequences
Why it matters
This objective helps connect Sequences to exam-style questions, flashcards, and revision notes for Pure Mathematics.
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Open revision notesRelated learning objectives
- A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs.
Proof
- B1 Understand and use the laws of indices for all rational exponents.
Laws of indices
- B2 Use and manipulate surds, including rationalising the denominator.
Surds
- B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown.
Quadratic functions
- B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.
Simultaneous equations