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1.6 Sequences and Series

1.6 Sequences and Series

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Question 130

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The concentrations of two enzymes, Enzyme A and Enzyme B, are being monitored in a laboratory bioreactor. Initially, there are 800 units of Enzyme A.

A model predicts that the quantity of Enzyme A will increase by 6% each hour, so that the number of units of Enzyme A at the end of each hour forms a geometric sequence.

a.

Find, according to the model, the number of units of Enzyme A in the bioreactor 12 hours after monitoring began. Give your answer to 3 significant figures.

[2]
b.

The quantity of Enzyme B is being monitored over the same period. Given that:

  • 2 hours after monitoring began there were 3200 units of Enzyme B
  • 5 hours after monitoring began there were 2400 units of Enzyme B
  • the quantity of Enzyme B at the end of each hour is modelled as a geometric sequence

Find the equation of this model in the form

N=abt N = ab^t N=abt

where NNN is the number of units of Enzyme B, ttt hours after monitoring began, and aaa and bbb are constants. Give the value of aaa and the value of bbb to 2 significant figures.

[4]
c.

When t=Tt = Tt=T, the quantity of Enzyme A is equal to the quantity of Enzyme B.

Find, according to the models, the value of TTT, giving your answer to one decimal place.

[4]
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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