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Sequences, recurrence relations and sigma notationEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

  • What is the difference between a position-to-term formula and a term-to-term rule?
  • What does a recurrence relation need in order to define a unique sequence?
  • Find u3 if u1=5 and u{n+1}=2un-3.
  • What is a fixed point of u{n+1}=f(un)?
  • Define an increasing sequence.
  • How can you prove un is decreasing?
  • Is un=\frac{1}{3n+1} increasing or decreasing?
  • What is a periodic sequence of order k?
  • u{n+1}=\frac{1}{un}, u1=3. Describe the sequence.
  • What does \sum{r=1}^{n}ur mean?
  • How many terms are in \sum{r=m}^{n}ur?
  • State \sum{r=1}^{n}1 and \sum{r=1}^{n}k.

Exam questions on Sequences, recurrence relations and sigma notation

  1. A sequence is defined by u1=5u_1=5 and un+1=2un−3u_{n+1}=2u_n-3 for n≥1n\ge1.
    Calculate ∑r=14ur\sum_{r=1}^{4}u_r.2 marks
  2. A sequence is defined by u1=2u_1=2 and un+1=8unu_{n+1}=\frac{8}{u_n} for n≥1n\ge1.
    Explain why the sequence is periodic and state its order.2 marks
  3. A sequence has nnth term un=n2−8n+20u_n=n^2-8n+20 for n≥1n\ge1.
    Show that un+1−un=2n−7u_{n+1}-u_n=2n-7, and hence find the values of nn for which un+1<unu_{n+1}<u_n.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).