Answer:
Please check the explanation.
Step-by-step explanation:
a)
A sequence is defined by the term-to-term rule such as
[tex]U_{n+1}=U^3_n+2[/tex]
Given that
[tex]U_0=-3[/tex]
Substituting n = 0 to determine u₁
[tex]U_{0+1}=U^3_0+2[/tex]
[tex]U_1=U^3_0+2[/tex]
substituting [tex]U_0=-3[/tex]
[tex]U_1=\left(-3\right)^3+2[/tex]
[tex]U_1=-27+2[/tex]
[tex]U_1=-25[/tex]
Therefore,
b)
[tex]U_{n+1}=U^3_n+2[/tex]
Substituting n = 1 to determine u₂
[tex]\:U_{1+1}=U^3_1+2[/tex]
substituting [tex]U_1=-25[/tex]
[tex]U_2=\left(-25\right)^3+2[/tex]
[tex]U_2=-15625+2[/tex]
[tex]U_2=-15623[/tex]
Therefore,
[tex]U_2=-15623[/tex]
