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If $x = \displaystyle\sum_{n=0}^{\alpha} a^n,y=\displaystyle\sum_{n=0}^{\alpha} b^n,z= \displaystyle\sum_{n=0}^{\alpha} c^n$ where $a, b, c$ are in AP and $|a| < 1, |b| < 1, |c|<1$, then $x, y, z$ are in :

( A ) AP
( B ) Arithmetrico-Geometric Progression
( C ) HP
( D ) GP

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