The difference between each term is -5, i.e. we know one of our terms is -5n. Now we just need to adjust it to get u1 correct. At n=1, -5n would give us -5 therefore we need to add 6 to get to 1. This gives us our equation:
[tex]\boxed{u_n=-5n+6}[/tex]
Now we can work out the sum easily (we can use an equation using the above but personally I prefer the other one as it's less prone to mistakes):
[tex]S_n= \frac{n}{2}(2u_1+(n-1)d) [/tex]
We know n is 12, and we know u1 is 1, and we also know the difference is -5.
Substituting this in:
[tex]S_{12}= \frac{12}{2}(2*1+(12-1)*-5)=6(2-55)=6*-53 \\ \boxed{S_{12}=-318} [/tex]
