An environmental group plants saplings in a reforestation zone. The number of saplings planted each week follows an arithmetic progression. In week 5, 38 saplings are planted. The total number of saplings planted across the first 12 weeks is $S_{12}=510$. Determine the number of saplings planted in week 1 and the common difference of the progression.

In a second reforestation zone, saplings are also planted weekly in an arithmetic progression. In the first week, 86 saplings are planted, and the number of saplings planted decreases by 5 each week. The sum of the first $n$ terms of this second progression is $T_n$. Let $S_n$ be the sum of the first $n$ terms of the first progression from part (a). Find the value of $n$ such that $T_n=S_n$, where $n>0$.