Show that `x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2,` are consecutive terms of an A.P., if `x ,y and z` are in A.P.

Explanation

To show that \( x^2 + xy + y^2 \), \( z^2 + xz + x^2 \), and \( y^2 + yz + z^2 \) are consecutive terms of an arithmetic progression (A.P.) when \( x, y, z \) are in A.P., we will follow these steps:

### Step 1: Understand the condition for A.P.
In an arithmetic progression, the middle term is the average of the first and third terms. Therefore, for three terms \( A, B, C \) to be in A.P., the condition is:
\[ 2B = A + C \]

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