Answer:
[tex]a_1=4\\\\a_2=0\\\\a_3=3[/tex]
Explanation:
The equation is:
[tex]a_n=3a_{n-1}-5a_{n-2}-4a_{n-3}[/tex]
and
[tex]a_4=-7, a_5=-36, a_6=-85[/tex]
1. Subsittute n = 6 into the equation:
[tex]a_6=3a_{5}-5a_{4}-4a_{3}[/tex]
Now subsititute the known values:
[tex]-85=3(-36)-5(-7)-4a_{3}[/tex]
You can solve for [tex]a_3[/tex]
[tex]-85=-108+35-4a_{3}\\\\4a_3=12\\\\a_3=12/4\\\\a_3=3[/tex]
2. Substitute n = 5 into the equation:
[tex]a_5=3a_{4}-5a_{3}-4a_{2}[/tex]
Substitute the known values and solve for [tex]a_2[/tex]
[tex]-36=3(-7)-5(3)-4a_{2}\\\\4a_2=-21-15+36=0\\\\a_2=0[/tex]
3. Substitute n = 4 into the equation, subsitute the known values and solve for [tex]a_1[/tex]
[tex]a_4=3a_{3}-5a_{2}-4a_{1}[/tex]
[tex]-7=3(3)-5(0)-4a_{1}\\\\4a_1=9+7=16\\\\a_1=4[/tex]
