Answer:
[tex]\huge\boxed{6,\ -30;\ 78;\ -246;\ 690}[/tex]
Step-by-step explanation:
[tex]a_1=6\\a_n=-3a_{n-1}-12\qquad n\geq2\\\\\text{Substitute}\ n=2,\ n=3,\ n=4,\ n=5\ \text{to}\ a_n=-3a_{n-1}-12:\\\\\text{for}\ n=2\\\\a_2=-3a_{2-1}-12=-3a_1-12\\\\\text{substitute}\ a_1=6\\\\a_2=-3(6)-12=-18-12=-30\\\\\text{for}\ n=3\\\\a_3=-3a_{3-1}-12=-3a_2-12\\\\\text{substitute}\ a_2=-30\\\\a_3=-3(-30)-12=90-12=78[/tex]
[tex]\text{for}\ n=4\\\\a_4=-3a_{4-1}-12=-3a_3-12\\\\\text{substitute}\ a_3=78\\\\a_4=-3(78)-12=-234-12=-246\\\\\text{for}\ n=5\\\\a_5=-3a_{5-1}-12=-3a_4-12\\\\\text{substitute}\ a_4=-246\\\\a_5=-3(-246)-12=702-12=690[/tex]
