Instructions

Let p,q be integers and let $$\alpha,\beta$$ be the roots of the equation, $$X^{2}-x-1=0$$, Where $$\alpha\neq\beta$$. For n=0,1,2..., Let $$a_{n}=p\alpha^{n}+q\beta^{n}$$.

FACT: If a and b are rational numbers and $$a+b\sqrt{5}=0$$, then $$a=0=b$$.

Question 53

$$a_{12}=$$

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JEE (Advanced) 2017 Paper-2

$$a_{12}=$$

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