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 ($p
e 0$). 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

$x_2 = p+1$, $x_3 = 1 + 3p + 2p^2$, $p = -\frac{3}{2}$, $x_{2008} = -\frac{1}{2}$

2008 A-Level Edexcel C1 January Q7

2008 A-Level Edexcel C1 January Q7

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