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1.6 Sequences and Series

1.6 Sequences and Series

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Question 132
a.

An arithmetic series is defined by the expression

∑r=837(4r−3) \sum_{r=8}^{37} (4r - 3) r=8∑37​(4r−3)

(i) Write down the first term of the series. (ii) Write down the common difference of the series. (iii) Find the number of terms of the series.

[3]
b.

The energy output of a turbine across various operating frequencies is modeled by a different arithmetic series

∑r=2079(kr+m) \sum_{r=20}^{79} (kr + m) r=20∑79​(kr+m)

where kkk and mmm are constants. The total energy output of this series is 10980 units. (i) Show that 49.5k+m=18349.5k + m = 18349.5k+m=183. (ii) The 21st term of the series is 15 more than twice the 1st term. Find the values of kkk and mmm.

[6]
Markscheme

1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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