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Sequences and Series

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Question 57

A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1​,u2​,u3​,… is defined by

u1=4un+1=kun+2,n≥1 \begin{aligned}u_1 &= 4 \\u_{n+1} &= ku_n + 2, \quad n \geq 1\end{aligned} u1​un+1​​=4=kun​+2,n≥1​
a.

Find an expression for u2 u_2\,u2​ in terms of kkk.

[1]
b.

Show that u3=4k2+2k+2u_3 = 4k^2 + 2k + 2u3​=4k2+2k+2.

[2]
c.

Given that u3=32u_3 = 32u3​=32, find the possible values of kkk.

[3]
Markscheme

Sequences and Series Questions

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

326 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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