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1.6 Sequences and Series

1.6 Sequences and Series

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Question 190

The initial phase of a biological growth process is modeled by the function B(t)=(2+κt4)7B(t) = \left( 2 + \frac{\kappa t}{4} \right)^7B(t)=(2+4κt​)7, where ttt is the time in hours and κ\kappaκ is a non-zero constant.

a.

Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of B(t)B(t)B(t). Give each term in simplest form.

[4]
b.

Given that, in the binomial expansion of B(t)B(t)B(t), the coefficients of ttt, t2t^2t2 and t3t^3t3 are the first three terms of an arithmetic progression,

find, using algebra, the possible values of κ\kappaκ.

[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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