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?
\[6,\,8,\,12,\,30,\,84\]
\[2,\,4,\,10,\,28,\,82\]
\[1,\,4,\,10,\,28,\,82\]
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 \({U_4}\).
\({U_2} = - 7\), \({U_3} = 11\), \({U_4} = - 25\)
\({U_2} = 7\), \({U_3} = - 11\), \({U_4} = 25\)
\({U_2} = 7\), \({U_3} = 11\), \({U_4} = 25\)
What is the limit of \({U_{n + 1}} = 0.6{U_n} + 7\) as \(n \to \infty\)?
\[\frac{{35}}{3}\]
\[\frac{{35}}{2}\]
\[7\]
A sequence is given by the recurrence relation \({U_{n + 1}} = 0.5{U_n} - 3\). If \({U_1} = 5\), find \({U_0}\) and \({U_{ - 1}}\).
\({U_0} = 4\), \({U_{ - 1}} = 8\)
\({U_0} = 8\), \({U_{ - 1}} = 16\)
\({U_0} = 16\), \({U_{ - 1}} = 38\)
If in a recurrence relation \({U_{n + 1}} = 0.2{U_n} + 4\) and \({U_0} = 6\), what does \({U_3}\) equal?
\[1.008\]
\[5.008\]
\[5.08\]
If in a recurrence relation \({U_{n + 1}} = 3{U_n} - 2\) and \({U_0} = - 5\), what does \({U_3}\) equal?
\[- 161\]
\[- 53\]
\[53\]
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?
\[5\]
\[8\]
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?
\[m = 1,\,k = - 3\]
\[m = 1,\,k = 3\]
\[m = - 3,\,k = 1\]
As \(n\) tends to infinity, what is the limit of the sequence defined by the recurrence relation \({U_{n + 1}} = 0.6{U_n} + 50\)?
\[50\]
\[125\]
\[300\]
As \(n\) tends to infinity, what is the limit of the sequence defined by the recurrence relation \({t_{n + 1}} = 0.75{t_n} + 200\)?
\[150\]
\[200\]
\[800\]