If $a_1, a_2, a_3,...., a_n,...$are in A.P. such that $a_4-a_7+a_{10}=m,$ then sum of the first 13 terms of the A.P. is 

Let d be the common difference of the A.P.,

then       $\begin{array}{l}m=a_4-a_7+a_{10}=a_4+\left(a_{10}-a_7\right)\\ =a_1+3d+3d=a_1+6d\end{array}$

Now,    $S_{13}=\frac{13}{2}\left[2a_1+(13-1)d\right]=13m.$