SOLUTION: the third term of an arithmetic sequence is 9. The sum of the next two terms is -18. Find the first two terms of the sequence; write a sequence formula and an explicit formula

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Question 853096: the third term of an arithmetic sequence is 9. The sum of the next two terms is -18. Find the first two terms of the sequence; write a sequence formula and an explicit formula
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
S = ½(a + an)n
-18 = ½(2a + d(n-1))n
9 = a + (2)d
S = ½(a + an)n
S = ½(2a + d(n-1))n
-18 = a + 3d+ a + 4d
-18 = 2a + 7d
9 = a + 2d
18 = 2a+4d
-18 = 2a + 7d
36=-3d
d=-12
9 = a + 2d
9=a+2*(-12)
9=a-24
33=a
d=-12
33,21,9,-3,-15,-27
a(n) = -3(4n-15)
a(n) = -12n-45
a(n)=33+(n-1)(-12)
a(n+1)n-12
(for all terms given)