We are given the following sequence:
[tex]6,-20,58[/tex]The formula that we can use to obtain the sequence is the following:
[tex]a_n=-3a_{n-1}-2,a_1=6[/tex]Because when we replace the given terms we get:
[tex]\begin{gathered} a_2=-3(6)-2 \\ a_2=-18-2 \\ a_2=-20 \end{gathered}[/tex]For the next term:
[tex]\begin{gathered} a_3=-3(-20)-2 \\ a_3=60-2 \\ a_3=58 \end{gathered}[/tex]