2026 RI Promo Q6

2026 RI Promo Q6

Junior College 1
8 marks
  1. A sequence \(u_1,u_2,u_3,\ldots\) is such that \(u_{n+1}=\dfrac1{11}u_n+\dfrac83\) for positive integers \(n\).
    1. Describe how the sequence behaves when \(u_1=5\).[1]
    2. It is given that as \(n\to\infty\), \(u_n\to l\). Find the exact value of \(l\).[2]
  2. It is given that \(\sum\limits_{r=1}^{n}r^2=\dfrac16n(n+1)(2n+1)\).
    Find \(\sum\limits_{r=7}^{3N}(6-2r)(r-1)\) in the form \(aN^3+bN^2+cN+d\), where \(a\), \(b\), \(c\) and \(d\) are integers to be determined.[5]

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Answer:(a)(i) Decreases to a limit. (ii) \(l=\dfrac{44}{15}\). (b) \(-18N^3+27N^2-7N+50\).

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