Answer:
[tex]a_4 = -108[/tex]
Step-by-step explanation:
Given
[tex]a_n = -3a_{n-1}[/tex]
[tex]a_1 = 4[/tex]
Required
Find [tex]a_4[/tex]
[tex]a_4 = -3a_{4-1}[/tex]
[tex]a_4 = -3a_3[/tex]
We calculate for a3
[tex]a_3 = -3a_{3-1}[/tex]
[tex]a_3 = -3a_2[/tex]
Calculate for a2
[tex]a_2 = -3a_{2-1[/tex]
[tex]a_2 = -3a_1[/tex]
Substitute 4 for a1
[tex]a_2 = -3*4[/tex]
[tex]a_2 = -12[/tex]
Substitute -12 for a2 in [tex]a_3 = -3a_2[/tex]
[tex]a_3 = -3 * -12[/tex]
[tex]a_3 = 36[/tex]
Substitute 36 for a3 in [tex]a_4 = -3a_3[/tex]
[tex]a_4 = -3*36[/tex]
[tex]a_4 = -108[/tex]
