SOLUTION: Find An for the arithmetic series with S16 =-288 and a1=-21

Question 681567: Find An for the arithmetic series with S16 =-288 and a1=-21
Answer by Jolliano(16) (Show Source): You can put this solution on YOUR website!
T16 = a +(16 - 1)d
T16 = 21 + (15)d Sn = (n/2)(a + l)
where l is the last term among the terms in the sum.
In the case our last term would be T16. Therefore
S16 = (16/2)(21 +[21 +15d]) = 288
(8)(21 + 21 + 15d) = 288
(21 + 21 + 15d) = 288/8
42 + 15d = 36
15d = 36 - 42 = -6
d = -6/15 = -2/5 = -0.4 Therefore,
An or Tn or Un = a + (n - 1)d
An or Tn or Un = 21 + (n -1)(-0.4)
= 21 - 0.4(n - 1)
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