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Show that the sequence defined by the formula a_n = n+3, satisfies the recurrence relation a_n = 2a_n-1 - a_n-2 ,for all n ≥ 2.

I know this is a induction problem and I think I have to set n= n+1 but I'm not sure that how would I show the recurrence relation between them.

Alex
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1 Answers1

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It is not an induction problem. We have $$2a_{n-1}-a_{n-2}=2(n-1+3)-(n-2+3)=n+3=a_n.$$

André Nicolas
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