This is an arithmetic sequence with a (first term)=7, common difference d=-4.
The sequence can be written a, a+d, a+2d, ..., a+(n-1)d where a+(n-1)d is the nth term.
We can rearrange this into pairs of terms:
(a+a+(n-1)d)+(a+d+a+(n-2)d)+...,
(2a+nd-d)+(2a+d+nd-2d)+...,
(2a+nd-d)+(2a+nd-d)+....
Because these pair-sums are identical and there are n/2 pairs, the sum of the series is:
Sn=(n/2)(2a+nd-d). Note that S1=½(14+0)=7, the first term. So the formula works even for odd n.
If a=7 and d=-4, S2=14-4=10 (n=2); S2=7+3=10.
When n=4, S4=2(14-12)=4; S4=7+3-1-5=4.
So, for a=7, d=-4 and n=50, S50=25(14+49×(-4))=25(14-196)=-4550.