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 \({t_{n + 1}} = 0.75{t_n} + 200\)?