If $S_1,S_2,S_3,\dots\dots,S_m$ are the sum of first $n$ terms of $m$ arithmetic progressions, whose first terms are $1,4,9,16,\dots,m^{2}$ and common differences are $1,2,3,4,\dots m$ respectively, then the value of $S_1+S_2+S_3+\dots \dots +S_m$ is :
- $\dfrac{mn(m+1)}{2} \\$
- $\dfrac{mn(2m+1)}{3} \\$
- $\dfrac{mn[3(m+1)+1]}{6} \\$
- $\dfrac{mn(m+1)(4m+3n-1)}{12}$