The finite order variational sequence (VS) is an effective tool for solving the problem of trivial Lagrangians and of the inverse problem. VS itself is a rather difficult mathematical problem, especially in global issues. Its deeper understanding requires adoption of the sheaf theory and solution of specific topological problems (cohomology). We present only elementary considerations concerning VS. VS is derived from the sequence of spaces of forms connected by the exterior derivative \(\textrm{d}\) . It is essential that \(\textrm{d}\circ \,\textrm{d}\) is zero, i.e. locally, a closed form is exact). To the sequence of \(\textrm{d}\) s between the spaces of forms corresponds the sequence of mappings between the factor-spaces obtained by factorization of spaces of forms with respect to some subspaces of specific contactness. In mechanics: to \(\textrm{d}\) assigning to 1-form \(\omega \) 2-form \(\textrm{d}\omega \) corresponds in VS the Euler-Lagrange (EL) mapping assigning to Lagrangians their EL forms, to d assigning to 2-form \(\omega \) 3-form \(\textrm{d}\omega \) corresponds the mapping assigning to EL forms their Helmholtz-Sonin (HS) forms, etc. Locally: the kernel of EL mapping is formed by trivial Lagrangians, the kernel of HS mapping is formed by variational dynamical forms, etc. Representation of mentioned mappings by forms is introduced via the interior Euler operator.