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1.7 D: Sequences and series

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Question 11

In a geometric sequence x1,x2,x3,…x_1, x_2, x_3, \dotsx1​,x2​,x3​,…:

  • the common ratio is rrr
  • x2+x3=9x_2 + x_3 = 9x2​+x3​=9
  • x4=6x_4 = 6x4​=6
a.

Show that r r\,r satisfies the equation

3r2−2r−2=0 3r^2 - 2r - 2 = 0 3r2−2r−2=0
[4]
b.

Given that the geometric sequence has a sum to infinity,

find the exact value of x1 x_1\,x1​ in the form a+b7a + b\sqrt{7}a+b7​ where a,b∈Qa, b \in \mathbb{Q}a,b∈Q.

[4]
c.

Hence, calculate the value of S∞S_\inftyS∞​.

[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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