# Interesting Sequence

**Algebra**Level 3

Consider the sequence \(\left\{a_{n}\right\}\) where \(a_{1}=0\) and \(a_{n+1}=a_{n}+1+2\sqrt{1+a_{n}}\) for natural numbers \(n\).

Find the value of \(a_{2009}\).

Consider the sequence \(\left\{a_{n}\right\}\) where \(a_{1}=0\) and \(a_{n+1}=a_{n}+1+2\sqrt{1+a_{n}}\) for natural numbers \(n\).

Find the value of \(a_{2009}\).

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