# Just like Fibonacci

Algebra Level 5

Let $$\{a_r\}$$ be a sequence of positive integers such that $$a_r = a_{r-1} + a_{r-2}$$ for $$r\ge3$$ and $$a_2=4$$. It is given that $$a_n+2a_{n-1}+a_{n-2}=123$$ (such that $$a_{n+2}$$is the last term of the sequence). Find the value of $\frac{1}{na_1}\sum _{ r=1 }^{ r=n }{ a_r } +\frac{4}{a_1}$

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