Answer:
a1= -2/9
a2= 4/3
a3= 6
Step-by-step explanation:
[tex]a_n = 3a_{n - 1} + 2[/tex]
a_4= 20
lets plug in 4 for n
[tex]a_4 = 3a_{4 - 1} + 2[/tex]
[tex]20= 3a_3+ 2[/tex]
Subtract 2 from both sides and then divide by 3
18 = 3a_3
[tex]6=a_3[/tex]
lets plug in 3 for n and use a3=6 to find a2
[tex]a_3 = 3a_{3 - 1} + 2[/tex]
[tex]6= 3a_2+ 2[/tex]
Subtract 2 from both sides and then divide by 3
4 = 3a_2
[tex]\frac{4}{3}=a_2[/tex]
lets plug in 2 for n and find out a1
[tex]a_2 = 3a_{2 - 1} + 2[/tex]
[tex]\frac{4}{3}= 3a_1+ 2[/tex]
Subtract 2 from both sides and then divide by 3
[tex]\frac{-2}{3}= 3a_1[/tex]
[tex]\frac{-2}{9}=a_1[/tex]
