2026 RSS P1 Q18

2026 RSS P1 Q18

Secondary 4
4 marks

The first four terms of a sequence of fractions are \(\dfrac23\), \(\dfrac58\), \(\dfrac8{13}\) and \(\dfrac{11}{18}\).

  1. Write down the next term in the sequence.[1]
  2. Find, in terms of \(n\), an expression for the \(n\)th term, \(T_n\).[1]
  3. Determine, showing your working, whether \(\dfrac{503}{800}\) can be a term of this sequence.[2]

Solution:

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Answer:(a) \(\dfrac{14}{23}\) (b) \(T_n=\dfrac{3n-1}{5n-2}\) (c) No: \(n=\dfrac{206}{115}\) is not an integer.

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