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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 180

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

u1=3u_1 = 3u1​=3

un+1=un+cu_{n+1} = u_n + cun+1​=un​+c, n≥1 n \geq 1\,n≥1

where c c\,c is a constant.

It is given that u5=23u_5 = 23u5​=23.

a.

Find the value of ccc.

[2]
b.

Find an expression for un u_n\,un​ in terms of nnn.

[2]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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