The difference between any given two successive terms is 5. So the sequence is an arithmetic progression.

a_1=4 and d=5

a_n=a_1+(n-1)d

=4+5(n-1)

=5n-1

Therefore, the general term of the sequence is a_n=5n−1. To calculate the 50^{th} partial sum of this sequence we need the 1st and the 50th terms:

a_1=4

a_{50}=5\times 50-1=249

Next use the formula to determine the 50^{th} partial sum of the given arithmetic sequence.

S_{50} = \dfrac{50(a_1+a_{50})}{2} =\dfrac{50(4+249)}{2}=6325

\therefore S_{50}=6325