BEIJING, Oct 15 (Reuters) - China’s factory gate prices fell in annual terms for the eighth straight month in September, official data showed on Thursday, while consumer inflation eased further. The producer price index fell 2.1% from a year earlier, according to a statement from the National Bureau of Statistics. This compared with a 2.0% drop in August and a forecast 1.8% decline in a Reuters poll of analysts. The statistics bureau also said the consumer price index rose 1.7% from a year earlier in September, compared with a 1.8% increase tipped by the Reuters poll and a 2.4% rise in August. (Reporting by Stella Qiu and Ryan Woo; Editing by Tom Hogue)