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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 199

In the calibration of a precision acoustic sensor, the signal response R(s)R(s)R(s) for a sensitivity parameter s s\,s is modeled by the function

R(s)=(2+ks4)5 R(s) = \left( 2 + \frac{ks}{4} \right)^5 R(s)=(2+4ks​)5

where k k\,k is a non-zero constant.

a.

Find the first 4 terms, in ascending powers of sss, of the binomial expansion of R(s)R(s)R(s). Give each term in its simplest form.

[4]
b.

An enhanced signal model is defined by

G(s)=(5+2s)(2+ks4)5 G(s) = (5 + 2s) \left( 2 + \frac{ks}{4} \right)^5 G(s)=(5+2s)(2+4ks​)5

In the series expansion of G(s)G(s)G(s), the coefficient of s s\,s is equal to the constant term. Find the value of kkk.

[3]
Markscheme

1.7 D: Sequences and series Questions

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

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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