\text { (a) Is } a_{n}=\frac{3 n+2}{n-4} \text { a general term of a sequence? Why? } \text { (b) Which term of the sequence with general term } \frac{3 n-1}{5 n+7} \text { is } \frac{7}{12} \text { ? } (c) An arithmetic sequence has its 4th term equal to 18 and its 12th term equal to 50. Find its 99th term. (d) State whether the following sequences are arithmetic, geometric or notany of them. Find the common ratio if it is a geometric sequence and findthe common difference d if it is an arithmetic sequence. Then, find thenext two terms.[6] \text { i. }-3,3,-3,3 \text { ii. } b_{n}=n^{2}+3 \text { iii. } \frac{-1}{2}, \frac{-5}{6}, \frac{-7}{6} (e) Consider the geometric sequence (bn) with b1 =1/9 and q =3 is 243 a term of sequence (f) The nineteenth term of a sequence is -52, and the fourth term is -7. The difference between consecutive terms in the sequence is constant. Find the 201st term. (g) Show whether the following sequence is convergent or divergent. \lim _{n \rightarrow \infty}\left(\frac{n-1}{n}\right) (h) Is the following numbers 1,-4,9,-16,... represent a sequence, if so, find a formula for the nth term of the sequence. (i) Show by mathematical induction that for all positive integers n, \frac{1}{2}+\frac{1}{2^{2}}+\ldots+\frac{1}{2^{n}}=1-\frac{1}{2^{n}} (i) Find the remainder when 3123 is divided by 7.