# Applications - Sequences test questions

### 1

A sequence is defined by the recurrence relation $${U_n}= 3{U_{n - 1}}- 2$$.

If $${U_0} = 2$$, what are the first five terms of the sequence?

### 2

A sequence is defined by the recurrence relation $${U_{n + 1}} = 3 - 2{U_n}$$.

If $${U_1} = - 2$$, calculate $${U_2}$$, $${U_3}$$ and $${U_4}$$.

### 3

What is the limit of $${U_{n + 1}} = 0.6{U_n} + 7$$ as $$n \to \infty$$?

### 4

A sequence is given by the recurrence relation $${U_{n + 1}} = 0.5{U_n} - 3$$. If $${U_1} = 5$$, find $${U_0}$$ and $${U_{ - 1}}$$.

### 5

If in a recurrence relation $${U_{n + 1}} = 0.2{U_n} + 4$$ and $${U_0} = 6$$, what does $${U_3}$$ equal?

### 6

If in a recurrence relation $${U_{n + 1}} = 3{U_n} - 2$$ and $${U_0} = - 5$$, what does $${U_3}$$ equal?

### 7

If a recurrence relation is defined by $${U_{n + 2}} = {U_{n + 1}} + {U_n}$$ and $${U_1} = 1$$ and $${U_2} = 1$$, what would the fifth term of the sequence be?

### 8

If the first three terms of a linear recurrence relation $${t_{n + 1}} = m{t_n} + k$$ are $$10$$, $$7$$, and $$4$$ in order, then what values do $$m$$ and $$k$$ have?

### 9

As $$n$$ tends to infinity, what is the limit of the sequence defined by the recurrence relation $${U_{n + 1}} = 0.6{U_n} + 50$$?

### 10

As $$n$$ tends to infinity, what is the limit of the sequence defined by the recurrence relation $${t_{n + 1}} = 0.75{t_n} + 200$$?