A-level · Sequences & series

Sigma notation and recurrence relationsExam-style questions

Reading and evaluating sums written with Σ, and generating sequences from a recurrence relation — including spotting periodic behaviour.

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27 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    A sequence is given by un+1=4−unu_{n+1} = 4 - u_n with u1=1u_1 = 1.
    (a) Find u2u_2, u3u_3 and u4u_4.
    (b) State the period of the sequence.
    (c) Hence find ∑r=150ur\displaystyle\sum_{r=1}^{50} u_r.
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