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1.6 Sequences and Series

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Question 37

An industrial kiln's control system modulates the internal temperature, TnT_nTn​ in degrees Celsius, at discrete time steps nnn. The temperature sequence T1,T2,T3,…T_1, T_2, T_3, \dotsT1​,T2​,T3​,… is defined by

Tn+1=1800−Tn T_{n+1} = 1800 - T_n Tn+1​=1800−Tn​

where T1=850T_1 = 850T1​=850 is the initial temperature reading.

Find the value of

a.

(i) T2T_2T2​

(ii) T121T_{121}T121​

[3]
b.

∑n=140(0.1Tn+5)\sum_{n=1}^{40} (0.1T_n + 5)∑n=140​(0.1Tn​+5)

[3]
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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