A sequence is given by: ${x_1 = 1,}$ ${x_{n+1} = x_n (p + x_n),}$ where $p$ is a constant

Question

A sequence is given by: ${x_1 = 1,}$ ${x_{n+1} = x_n (p + x_n),}$ where $p$ is a constant ($p\ne 0$). Find ${{x}_{2}}$ in terms of $p$.[1] Show that ${{x}_{3}}=1+3p+2{{p}^{2}}$.[2] Given that ${{x}_{3}}=1$, find the value of $p$.[3] Write down the value of ${{x}_{2008}}$.[2]

Accepted Answer

**(a)** ${x_2 = p + 1}$ **(b)** ${x_3 = 1 + 3p + 2p^2}$ **(c)** ${p = -\frac{3}{2}}$ **(d)** ${x_{2008} = -\frac{1}{2}}$

2008 A-Level Edexcel C1 January Q7

2008 A-Level Edexcel C1 January Q7

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