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Sequences and Series

Sequences and Series

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Question 93

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

Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /Sequences and Series

178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.

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