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3.3 Sequences and series (A-level only)

3.3 Sequences and series (A-level only)

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Question 27

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

3.3 Sequences and series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.3 Sequences and series (A-level only)

200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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