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

Answer:

Please check the explanation.

Step-by-step 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,

$U_2=-15623$