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A sequence is defined by the term-to-term rule
U = + 2
Given that u, = -3,
a) find u,
b) find uz

A Sequence Is Defined By The Termtoterm Rule U 2 Given That U 3 A Find U B Find Uz class=

Sagot :

absor201

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,

  • [tex]U_1=-25[/tex]

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]

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