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1.6 Sequences and Series

1.6 Sequences and Series

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Question 108

In a biological study, the population density P P\,P of a specific bacterial colony is modeled by the function P(c)=(4+kc)7P(c) = (4 + kc)^7P(c)=(4+kc)7, where c c\,c represents the concentration of a growth medium and k k\,k is a positive constant.

a.

Find the first three terms, in ascending powers of ccc, in the expansion of

(4+kc)7 (4 + kc)^7 (4+kc)7
[3]
b.

Given that the coefficient of c2 c^2\,c2 in this expansion is exactly half the coefficient of ccc, determine the value of the constant kkk.

[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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