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Question Number 90217 by Maclaurin Stickker last updated on 22/Apr/20

$$let{x}_{n}beasequencewith{x}_0=2and{x}_1=7$$$$and{x}_{n+1}=7x_n-12x_{n-1}.$$$$Findthegeneraltermof{x}_n.$$

Commented by jagoll last updated on 22/Apr/20

$${\mathrm{p}}^2-7\mathrm{p}+12=0$$$$\mathrm{p}=3\wedge \mathrm{p}=4$$$${\mathrm{x}}_{\mathrm{n}}=\mathrm{A}.3^{\mathrm{n}}+\mathrm{B}.4^{\mathrm{n}}$$$$\mathrm{n}=0\Rightarrow 2=\mathrm{A}+\mathrm{B}$$$$\mathrm{n}=1\Rightarrow 7=3\mathrm{A}+4\mathrm{B}$$$$\mathrm{B}=1\wedge \mathrm{A}=1$$$$\therefore {\mathrm{x}}_{\mathrm{n}}=1.3^{\mathrm{n}}+1.4^{\mathrm{n}}=3^{\mathrm{n}}+4^{\mathrm{n}}$$

Commented by Maclaurin Stickker last updated on 22/Apr/20

$$thankyou$$

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