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Tim Gan Math

2009 A-Level H2 Mathematics

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Question 1System of Linear Equations6 marks
  1. The first three terms of a sequence are given by ${{u}_{1}}=10$, ${{u}_{2}}=6$, ${{u}_{3}}=5$. Given that ${{u}_{n}}$ is a quadratic polynomial in $n$, find ${{u}_{n}}$ in terms of $n$.

    [4]

  2. Find the set of values of $n$ for which ${{u}_{n}}$ is greater than $100$.

    [2]

Solution step 1, image 1
Solution step 2, image 1

Final Answer:

(i) $u_n = \dfrac{3}{2}n^2 - \dfrac{17}{2}n + 17$ (ii) $\{n \in \mathbb{Z}^+ : n \geq 11\}$