Question19. (a) These are the first four terms in a sequence. (i) Find an expression, in terms of $n$, for the $n^{\text {th }}$ term of the sequence. $$\begin{array}{l} 23+(4 \times n) \\ \begin{array}{ll} & 23+(4 \times n) \\ \text { Answer } \end{array} \end{array}$$ (ii) Explain why it is not possible for a term in the sequence to be a multiple of 8 .
Answer $\qquad$ $\qquad$ [1] (iii) Write down the first four terms of a sequence in which some, but not all, of the terms are multiples of 8 .
Answer $\qquad$ [2] (b) The $n^{\text {th }}$ term of a difference sequence is given by $T_{n}=\frac{5 n+4}{192-4 n}$. (i) Use the formula to find $T_{5}$.
Give your answer as a fraction in its simplest form.
Answer $\qquad$ [1] (ii) The value of $T_{k}$ can be simplified to $\frac{4}{9}$. Find the value of $k$.
Answer $\qquad$ [3] (iii) Suggest a value of $n$ such that the value of $T_{n}$ is greater than 1 .