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1.7 D: Sequences and series

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Question 228

A signal processor's response function R(x)R(x)R(x) is defined by the expansion of R(x)=(2x−5)8R(x) = (2x - 5)^8R(x)=(2x−5)8.

a.

Show that the first three terms, in descending powers of xxx, of this expansion are given by

256x8+ax7+bx6 256x^8 + ax^7 + bx^6 256x8+ax7+bx6

where aaa and bbb are integers to be found.

[3]
b.

Find the constant term in the expansion of

(2x−5x)8 \left(2x - \frac{5}{x}\right)^8 (2x−x5​)8
[3]

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.

Question bank