Answer:
see explanation
Step-by-step explanation:
Given the recursive formula
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] + 2 and a₄ = 20
Then working in reverse
3a₃ + 2 = 20 ( subtract 2 from both sides )
3a₃ = 18 ( divide both sides by 3 )
a₃ = 6
3a₂ + 2 = 6 ( subtract 2 from both sides )
3a₂ = 4 ( divide both sides by 3 )
a₂ = [tex]\frac{4}{3}[/tex]
3a₁ + 2 = [tex]\frac{4}{3}[/tex] ( subtract 2 from both sides )
3a₁ = - [tex]\frac{2}{3}[/tex] ( divide both sides by 3 )
a₁ = - [tex]\frac{2}{9}[/tex]
Hence
a₁ = - [tex]\frac{2}{9}[/tex]
a₂ = [tex]\frac{4}{3}[/tex]
a₃ = 6
