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1.7 D: Sequences and series

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Question 137

The calibration of a specialized velocity sensor C(v)C(v)C(v), where v v\,v represents a small change in velocity from a reference state, is modeled by the function:

C(v)=15(25+kv)−12 C(v) = 15(25 + kv)^{-\frac{1}{2}} C(v)=15(25+kv)−21​

Given that the binomial expansion of C(v)C(v)C(v) in ascending powers of v v\,v is P−0.12v+Rv2+…P - 0.12v + Rv^2 + \dotsP−0.12v+Rv2+…

a.

find the values of the constants kkk, PPP, and RRR.

[4]
b.

State the range of values of v v\,v for which this expansion is valid.

[1]
c.

For this expansion, find the coefficient of the term in v3v^3v3.

[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.

Question bank