For the first time in several years, sales tax collections in the District of Columbia rose in 1978 faster than the rate of inflation and represented a real economic gain, the D.C. Department of Finance and Revenue reported.

Taxable sales increased 11.4 percent to a total of $149.2 million, representing a real growth rate of 3.7 percent after discounting for inflation, finance director Kenneth Back said.

The tax collections were levied at various tax rates on sales that totaled $2.8 billion, the department reported. The sales for 1977 were $2.5 billion.

Although sales tax collections over the years have grown, they had dropped below the pace of inflation and thus represented economic sluggishness or even losses. In 1977, taxable sales grew by 5.8 percent above the previous year, while they rose 3.4 percent in 1976 over 1975.

Back said last years's record increase "appears to be a sign that the (city's) economy is on the upswing."

Officials said the increases were listed in three major categories, including one not widely recognized as a source of sales tax revenues-taxes collected on building materials and equipment used for commercial and housing construction. Collections in that area were up 19.3 percent to nearly $8.5 million.

Other above-average increases were in tourist-related sales such as taxes on hotel and motel rooms (up 13.8 percent to $17.3 million) and sales by specialty businesses, such as book stores, barber and beauty shops, mailing, copying and stenographic services, photographers and artists. The latter were not statistically grouped into one tax catagory.