\(190-\left(a-1\right).a\div2+1=170\)
\(190-\left(a-1\right).a\div2=170-1\)
\(190-\left(a-1\right).a\div2=169\)
\(\left(a-1\right).a\div2=190-169\)
\(\left(a-1\right).a\div2=21\)
\(\left(a-1\right).a=21.2\)
\(\left(a-1\right).a=42\)
\(\left(a-1\right).a=6.7\)
\(\Rightarrow a=7\)