# Enjoy the sequence!

**Number Theory**Level 4

\[\large \sqrt{a_{2}+a_{3}+\cdots+a_{99}}-\sqrt{a_{1}+a_{100}} \]

Let \(a_{1},a_{2},a_{3},\ldots,a_{100}\) is an sequence of consecutive positive integers.

Find the minimum integer value of the expression above. of \ which is an integer.