Simple but nice #1

Calculus Level 3

\( x_1, x_2, \ldots x_n \) are non-zero real numbers that satisfy

\[ (x_{1}^2 + x_{2}^2 + x_{3}^2 +..... +x_{n+1}^2)(x_{2}^2 + x_{3}^2 + ... + x_{n}^2) \leq (x_{1}x_{2} + x_{2}x_{3} + .... + x_{n-1}x_{n})^2. \]

What kind of sequence does \(x_{1},x_{2},x_{3},...x_{n}\) form?

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