Question

Consider the sequence 10, 2..

Answer 1

Answer:  see below

Step-by-step explanation:

1) 10, 2, 1.2, 1.12, 1.112, 1.1112

$t_n=\dfrac{t_{n-1}}{10}+1$

t₁ = 10

t₂ = 10/10 + 1    = 2

t₃ = 2/10 + 1     = 1.2

t₄ = 1.2/10 + 1   = 1.12

t₅ = 1.12/10 + 1  = 1.112

t₆ = 1.112/10 + 1 = 1.1112

2)  10, 2, -2, -4, -5, -5.5, ...

$t_n=\dfrac{t_{n-1}}{2}-3$

t₁ = 10

t₂ = 10/2 - 3 =   2

t₃ = 2/2 - 3  =  -2

t₄ = -2/2 - 3 =  -4

t₅ = -4/2 - 3 =  -5

t₆ = -5/2 - 3 = -5.5