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1.6 Sequences and Series

1.6 Sequences and Series

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Question 145

The concentration of a specific catalyst, CnC_nCn​ mmol/L, in a chemical reactor is recorded every hour. The process is modeled by the recurrence relation

Cn+1=15−Cn,n≥1 C_{n+1} = 15 - C_n, \quad n \ge 1 Cn+1​=15−Cn​,n≥1

where the initial concentration is C1=4.5C_1 = 4.5C1​=4.5.

a.

Find the value of (i) C2C_2C2​ (ii) C85C_{85}C85​

[3]
b.

Determine the value of ∑n=1100(4Cn−5)\sum_{n=1}^{100} (4C_n - 5)∑n=1100​(4Cn​−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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