Step 1: Given $a = 4$, $a_n = l = 31$, $S_n = 175$.
Step 2: Use $$S_n = \frac{n}{2}(a + l)$$
Step 3: $$175 = \frac{n}{2}(4 + 31) = \frac{35n}{2}$$
$$350 = 35n \Rightarrow n = 10$$
Step 4: Now use $a_n = a + (n-1)d$ :
$$31 = 4 + (10-1)d \Rightarrow 27 = 9d \Rightarrow d = 3$$
Hence, number of terms $= 10$ and common difference $= 3$.