Question 3976
The partial sum of the first n terms of an arithmetic series whose first term is a1 is given by:

Sn = (n/2)(a1 + an)  We don't have a1 but we can get it from the formula for the nth term of an arithmetic sequence:  

an = a1 + (n - 1)d 
a9 = a1 + (9 - 1)(-4)        Substitute a9 =  27
27 = a1 + (8)(-4)
27 = a1 - 32                Add 32 to both sides.
a1 = 59

Now we can find S9

S9 = (9/2)(a1 + a9)         Substitute a1 = 59 and a9 = 27
S9 = (9/2)(59 + 27)
S9 = (9/2)(86)
S9 = 9(43)
S9 = 387