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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 148

The population P(t)P(t)P(t), in thousands, of a species in a controlled environment is estimated using the model P(t)=15(25+At)−12\displaystyle P(t) = 15(25 + At)^{-\frac{1}{2}}P(t)=15(25+At)−21​, where t t\,t is the time in years since the study began (t≥0t \ge 0t≥0). The binomial expansion of P(t)P(t)P(t) in ascending powers of t t\,t is given as B−625t+Ct2+…\displaystyle B - \frac{6}{25}t + Ct^2 + \dotsB−256​t+Ct2+…

a.

Determine the exact values of the constants AAA, BBB, and CCC.

[5]
b.

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

[1]
c.

For the expansion, find the coefficient of the term in t3t^3t3.

[2]
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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