Find the term(s) indicated in the below case:

$T_n=\frac{T_{n-1}}{T_{n-2}}\left(n>2\right), T_1=1; T_2=2; T_6$

Write the first five terms of the following sequence and obtain the corresponding series:

$a_1=3, a_n=3a_{n-1}+2$ for all $n>1$

Write the first five terms of the following sequence and obtain the corresponding series:

$a_1=-1, a_n=\frac{a_{n-1}}{n}, n\ge 2$

Write the first five terms of the following sequence and obtain the corresponding series:

$a_1=a_2=2, a_n=a_{n-1}-1, n>2$

Write the first six terms of the following sequence:

$a_1=-1, a_n=\frac{a_{n-1}}{n}, \left(n\ge 2\right)$

Write the first six terms of the following sequence:

$a_1=4, a_{n+1}=2n{a}_n$

Write the first six terms of the following sequence:

$a_1=\frac{1}{2}, a_2=-1, a_{n+2}=a_n{a}_{n+1}$

Write the first six terms of the following sequences:

$a_1=a_2=2, a_n=a_{n-1}-1, \left(n>2\right)$

The sequence $a\left(n\right)$ is defined by: $a\left(n\right)=(n-1)(n-2)(n-3)$. Show that the first three terms of the sequence are zero, but the rest of the terms are positive.