2026 YTSS P2 Q5

2026 YTSS P2 Q5

Secondary 4
7 marks
  1. The first four terms in a sequence are 5, 8, 11 and 14.
    1. Find the fifth term of the sequence.[1]
    2. \(T_n\) is the \(n\)th term of the sequence.
      Find an expression, in terms of \(n\), for \(T_n\).[1]
    3. \(T_{n^2}-T_n\) is a positive integer.
      Show that \(T_{n^2}-T_n\) is a multiple of 3 for \(n\geq a\). Hence, state the value of \(a\).[2]
    1. The first four terms in a different sequence are
      \(\dfrac51,\dfrac84,\dfrac{11}{9},\dfrac{14}{16}\)
      Find \(P_n\), the \(n\)th term of this sequence.[1]
    2. Jenna states that \(\dfrac{110}{289}\) is a term in the above sequence.
      Do you agree with her? Show your working clearly.[1]
    3. Explain why \(P_n\leq5\) for all values of \(n\).[1]

Solution:

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Answer:(a)(i) 17 (ii) \(3n+2\) (iii) \(3n(n-1)\), \(a=2\). (b)(i) \((3n+2)/n^2\) (ii) No (iii) \(3/n+2/n^2\leq5\).

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