Question

A sequence is defined by the term-to-term rule

U = + 2
Given that u, = -3,
a) find u,
b) find uz

Answer 1

Please check the explanation.

Explanation:

a)

A sequence is defined by the term-to-term rule such as

`U_(n+1)=U^3_n+2`

Given that

`U_0=-3`

Substituting n = 0 to determine u₁

`U_(0+1)=U^3_0+2`

`U_1=U^3_0+2`

substituting
`U_0=-3`

`U_1=\left(-3\right)^3+2`

`U_1=-27+2`

`U_1=-25`

Therefore,

• 
  `U_1=-25`

b)

`U_(n+1)=U^3_n+2`

Substituting n = 1 to determine u₂

`\:U_(1+1)=U^3_1+2`

substituting
`U_1=-25`

`U_2=\left(-25\right)^3+2`

`U_2=-15625+2`

`U_2=-15623`

Therefore,

`U_2=-15623`