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Question Number 92557 by I want to learn more last updated on 07/May/20

$$\mathrm{If}{\mathrm{a}}_1=5,{\mathrm{a}}_2=13\mathrm{and}{\mathrm{a}}_{\mathrm{n}+2}={5\mathrm{a}}_{\mathrm{n}+1}-{6\mathrm{a}}_{\mathrm{n}}.$$$$\mathrm{Find}{\mathrm{a}}_{\mathrm{n}}$$

Commented by prakash jain last updated on 07/May/20

$$a_{n+2}-5a_{n+1}+6a_n=0$$$$\mathrm{characteristic}\mathrm{equation}.$$$${\lambda }^2-5\lambda +6=0$$$$\lambda =2,3$$$$a_n=c_1{2}^n+c_2{3}^n$$$$a_1=5$$$$2c_1+3c_2=5$$$$a_2=13$$$$4c_1+9c_2=13$$$$\Rightarrow c_1=1,c_2=1$$$$a_n=2^n+3^n$$

Commented by I want to learn more last updated on 08/May/20

$$\mathrm{I}\mathrm{appreciate}\mathrm{sir}.$$

Commented by I want to learn more last updated on 08/May/20

$$\mathrm{Sir},\mathrm{which}\mathrm{book}\mathrm{can}\mathrm{i}\mathrm{learn}\mathrm{this}.$$

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