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1.7 D: Sequences and series

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Question 70

The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21​ are given by

(16+5x)12≈a+58x−25512x2 (16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2 (16+5x)21​≈a+85​x−51225​x2

where aaa is a constant.

a.

State the range of values of xxx for which this expansion is valid.

Choose from the options below:

∣x∣<516∣x∣<165∣x∣<4∣x∣<1 |x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1 ∣x∣<165​∣x∣<516​∣x∣<4∣x∣<1
[2]
b.

Find the value of aaa.

Choose from the options below:

14816 1 \quad 4 \quad 8 \quad 16 14816
[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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