is the term (in tensor notation)

A_i_j B_j_k S_k_i

equivalent to :

( A_i_1 B_1_k + A_i_2 B_2_k + A_i_3 B_3_k ) S_k_i

or if not can someone shed some light how to calculate the above mentioned terms

There will be 27 terms in all since each of i, j, k are repeated and each index will take values 1,2,3. For every selection of two of the indices let the third index cycle through all its 3 values. For instance you could fix i and j and let k vary and then repeat the procedure for all 9 choices for i and j.

It is equal to the following triple sum, where each summation is over the entire range of the index value

∑_i ∑_j ∑_kA_ij B_jk S_ki

If the indices vary over 1,2,3 then there are 27 terms in the above sum. The resultant is a scalar quantity.

thanks people, if it will have 27 quantities then i have calculated it right, wanted to check with others, thanks again.