A recurrence relation is a sequence that gives you a connection between two consecutive terms. This connection can be used to find next/previous terms, missing coefficients and its limit.

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

\[150\]

\[200\]

\[800\]