BEIJING, Jan 1 (Reuters) - Growth in China's services sector picked up slightly in December, a government study showed on Thursday, helping to offset further weakness in manufacturing which is weighing on the world's second-largest economy.

The official non-manufacturing Purchasing Managers' Index, or PMI, rose to 54.1 in December from November's 53.9, well above the 50-point line that separates growth from contraction on a monthly basis.

A similar activity study showed growth in China's factory sector slowed as expected in December, underlining the challenges facing the government as it tries to avert a sharper economic slowdown.

Many analysts expect economic growth in the fourth quarter to slow marginally from 7.3 percent in the third quarter, suggesting full-year growth will undershoot the government's 7.5 percent target and mark the weakest expansion in 24 years.

(Reporting by Judy Hua and Ben Blanchard; Editing by Kim Coghill)