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1.7 D: Sequences and series

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Question 172

A model for the energy output, E(x)E(x)E(x), of a specialized transducer under mechanical stress is defined by the function E(x)=(3+4x)4E(x) = (3 + 4x)^4E(x)=(3+4x)4, where xxx is the applied strain. The expansion of this function is given by

(3+4x)4=A+Bx+864x2+768x3+256x4 (3 + 4x)^4 = A + Bx + 864x^2 + 768x^3 + 256x^4 (3+4x)4=A+Bx+864x2+768x3+256x4
a.

Find the values of the constants AAA and BBB.

[2]
b.

Show that

(3+4x)4−(3−4x)4=Cx+Dx3 (3 + 4x)^4 - (3 - 4x)^4 = Cx + Dx^3 (3+4x)4−(3−4x)4=Cx+Dx3

where CCC and DDD are constants to be found.

[3]
c.

Hence, or otherwise, find

∫((3+4x)4−(3−4x)4)dx \int \left( (3 + 4x)^4 - (3 - 4x)^4 \right) dx ∫((3+4x)4−(3−4x)4)dx
[2]

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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