As you can notice, this sequence is detailed as follows:
[tex]\begin{gathered} 1\cdot1=1 \\ 1\cdot2=2 \\ 2\cdot3=6 \\ 6\cdot4=24 \end{gathered}[/tex]Now, let's find the next four terms:
[tex]\begin{gathered} 24\cdot5=120 \\ 120\cdot6=720 \\ 720\cdot7=5040 \\ 5040\cdot8=40320 \end{gathered}[/tex]A possible formula could be:
[tex]a_n=n\cdot a_{n-1}[/tex]Where "n" is the number of the term given and it starts from 1. (a0 is 1) This is:
[tex]\begin{gathered} a_1=1.a_{1-1}=1\cdot a_0=1_{} \\ a_2=2\cdot a_{2-1}=2\cdot a_1=2 \\ a_3=3\cdot a_{3-1}=3\cdot a_2=6 \\ \text{and so on } \end{gathered}[/tex]