2026 MSHS P2 Q7

2026 MSHS P2 Q7

Secondary 4
11 marks
  1. The first four terms of a sequence are shown below.
    \(\begin{aligned} T_1&=1^2+3=4 \\ T_2&=2^2+6=10 \\ T_3&=3^2+9=18 \\ T_4&=4^2+12=28 \end{aligned}\)
    1. Write down \(T_5\) in similar form.[1]
    2. Find an expression, in terms of \(n\), for \(T_n\).[1]
    3. Explain why \(T_n\) is always even for all positive integer values of \(n\).[2]
    4. Show that \(T_n=2T_{n-1}-T_{n-2}+2\) for all integers \(n\).[3]
  2. The \(n\)th term of another sequence is given by \(T_n=\dfrac{n^2+4}{4n-1}\).
    The term \(T_k=\dfrac83\).
    Find the value of \(T_{k+2}\).[4]

Solution:

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Answer:(a)(i) \(T_5=5^2+15=40\) (ii) \(T_n=n^2+3n\) (iii) One factor of \(n(n+3)\) is even. (iv) Identity shown. (b) \(3\dfrac7{47}\).

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