# Which inequality?

**Algebra**Level 4

If \(x_1,~x_2,~x_3,\dots,x_n\) are \(n\) non-zero real numbers such \[(x_1^2+x_2^2+x_3^2+\dots+x_{n-1}^2)(x_2^2+x_3^2+x_4^2+\dots+x_n^2)\leq(x_1x_2+x_2x_3+x_3x_4+\dots+x_{n-1}x_n)^2\] then \(x_1,~x_2,~x_3,\dots,x_n\) are in

**Note**:

- AP denotes an arithmetic progression.

- AGP denotes an arithmetic geometric progression.

- GP denotes an geometric progression.

- HP denotes an harmonic progression.