ÒrdughanA' fuasgladh dàimhean tillteachais loidhneach

Tha òrdugh air a mhìneachadh leis an dàimh tillteachais \({U_n} = m{U_{n - 1}} + c\)

Obraich a-mach na luachan aig \(m\) agus \(c\) ma tha \({U_1} = - 3\), \({U_2} = 7\) agus \({U_3} = 10\).

\({U_n} = m{U_{n - 1}} + c\)

An toiseach, obraich leis an dàimh tillteachais a chaidh a thoirt dhut agus ionadaich a-steach na luachan airson \({U_1}\), \({U_2}\) agus \({U_3}\)

\({U_2} = m{U_1} + c \Rightarrow 7\)

\(= m( - 3) + c \Rightarrow - 3m + c = 7\)

\({U_3} = m{U_2} + c \Rightarrow 10\)

\(= m(7) + c \Rightarrow 7m + c = 10\)

Fuasgail a-nis na co-aontaran \(- 3m + c = 7\) agus \(7m + c = 10\) gu co-amail.

\(- 10m = - 3\)

\(m = 0.3\)

\(7m + c = 10\). Ionadaich an luach seo airson \(m\) ann an aon dhe na co-aontaran gu h-àrd agus obraich a-mach luach \(c\).

\(7(0.3) + c = 10\)

\(c = 10 - 2.1\)

\(c = 7.9\)

Cleachd a-nis na luachan seo agus obraich a-mach \({U_4}\) agus \({U_0}\).

An toiseach, cuir na luachan aig \(m\) agus \(c\) dhan dàimh tillteachais, a' toirt \({U_n} = 0.3{U_{n - 1}} + 7.9\).

Cleachd a-nis an dàimh seo agus obraich a-mach \({U_4}\) agus \({U_0}\).

Gus \({U_4}\) obrachadh a-mach, cleachd \({U_3}\) agus gus \({U_0}\) obrachadh a-mach, cleachd \({U_1}\).

\({U_4} = 0.3{U_3} + 7.9\)

\(= 0.3(10) + 7.9\)

\(= 10.9\)

\({U_1} = 0.3{U_0} + 7.9\)

\(- 3 = 0.3{U_0} + 7.9\)

\(0.3{U_0} = - 3 - 7.9\)

\(0.3{U_0} = - 10.9\)

\({U_0} = - \frac{{109}}{3}\)

\({U_4} = 10.9\) agus \({U_0} = - \frac{{109}}{3}\)