Which inequality?

Algebra Level 4

If x1, x2, x3,,xnx_1,~x_2,~x_3,\dots,x_n are nn non-zero real numbers such (x12+x22+x32++xn12)(x22+x32+x42++xn2)(x1x2+x2x3+x3x4++xn1xn)2(x_1^2+x_2^2+x_3^2+\dots+x_{n-1}^2)(x_2^2+x_3^2+x_4^2+\dots+x_n^2)\leq(x_1x_2+x_2x_3+x_3x_4+\dots+x_{n-1}x_n)^2 then x1, x2, x3,,xnx_1,~x_2,~x_3,\dots,x_n are in

Note:
- AP denotes an arithmetic progression.
- AGP denotes an arithmetic geometric progression.
- GP denotes an geometric progression.
- HP denotes an harmonic progression.

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