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IP1U7 Exercise Q8

IP1U7 Exercise Q8

TGM Original Questions
  1. These are the first four terms in a sequence.
    \({ 23 \qquad 31 \qquad 39 \qquad 47 }\)
    1. Find an expression, in terms of \(n\), for the \({{n}^{\mathrm{th}}}\) term, \({{T}_{n}}\), of this sequence.
    2. Explain why it is not possible for a term in the sequence to be a multiple of \(8\).
  2. The \({{n}^{\mathrm{th}}}\) term of a different sequence is given by \({{T}_{n}}=\frac{3n+8}{108-2n}\).
    1. Find \({{T}_{5}}\). Give your answer as a fraction.
    2. The value of \({{T}_{k}}\) can be simplified to \(\frac{7}{18}\). Find the value of \(k\).
    3. Find the least value of \(n\) for which \({{T}_{n}}>1\).
    4. Find the greatest value of \(n\) for which \({{T}_{n}}>0\).

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Answer:(a)(i) \(T_n=8n+15\). (ii) Every term has remainder 7 on division by 8. (b)(i) \(23/98\). (ii) \(k=9\). (iii) \(21\). (iv) \(53\).

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