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Sequences and Series

Quick questions on Recurrence relations explained: H2 Mathematics Sequences and Series

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is finding a limiting value?
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If the sequence converges to a limit LL, then both unu_n and un+1u_{n+1} approach LL. Substitute LL for both in the recurrence and solve the resulting equation. For un+1=aun+bu_{n+1} = au_n + b this gives L=b1−aL = \dfrac{b}{1 - a}, valid when ∣a∣<1|a| < 1 so the sequence actually converges.
What is arithmetic slips in iteration?
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Each new term depends on the previous, so one error propagates; work carefully.
What is q1?
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Generate the first four terms of u1=5u_1 = 5, un+1=2un−3u_{n+1} = 2u_n - 3. [2 marks]
What is q2?
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A sequence has un+1=0.4un+6u_{n+1} = 0.4u_n + 6. Find its limit. [3 marks]
What is q3?
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State whether un+1=un+7u_{n+1} = u_n + 7 defines an arithmetic or geometric progression, and give the relevant parameter. [1 mark]

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