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1.4 Sequences and Series

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Question 43

The sum to infinity of a geometric series is 108. The first term of the series is less than 40. The second term of the series is 24.

a.

Find the first term and the common ratio of the series.

[4]
b.

Show that the n n\,nth term of the series, unu_nun​, can be written as un=2n+13n−3u_n = \dfrac{2^{n+1}}{3^{n-3}}un​=3n−32n+1​.

[2]
c.

Hence show that log⁡3un=n(log⁡32−1)+log⁡32+3\log_3 u_n = n\left(\log_3 2 - 1\right) + \log_3 2 + 3log3​un​=n(log3​2−1)+log3​2+3.

[2]
Markscheme

1.4 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.4 Sequences and Series

308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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