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Sequences and Series

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Question 105

The first term of the series is 36. The common ratio of the series is 2/32/32/3.

a.

Find the sum to infinity and the second term of the series.

[5]
b.

(i) Show that the n n\,nth term of the series, unu_nun​, can be written as un=2n+13n−3\displaystyle u_n = \frac{2^{n+1}}{3^{n-3}}un​=3n−32n+1​. (ii) Hence show that log⁡3un=n(log⁡32−1)+log⁡32+3\log_3 u_n = n(\log_3 2 - 1) + \log_3 2 + 3log3​un​=n(log3​2−1)+log3​2+3.

[7]
Markscheme

Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /Sequences and Series

326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.

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