SOLUTION: I need help on this problem. Thankx What is Sn for the arithmetic series with d = -4, an = 27, and n = 9?

Question 3976: I need help on this problem. Thankx
What is Sn for the arithmetic series with d = -4, an = 27, and n = 9?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
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

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