6. The 9th is 55
6. 【Solution】The first term of this sequence is 3, the second term is 3 more than the first term, and each subsequent term is 1 more than the previous increment, so the 9th term is $3+3+4+5+6+\cdots+10=1+2+3+4+5+6$ $+\cdots+10=55$.
6. As shown in the right figure, using equilateral triangles of the same size, larger equilateral triangles are sequentially assembled downward. The number of vertices of the smallest triangles (overlapping vertices are counted only once) are: $3, 6, 10, 15, 21, \cdots$ What is the 9th number in this sequence?