SOLUTION: the sum of the first fifteen terms of an arithmetic terms progression is 270. find the first term and the common difference if the the fifteenth terms is 39.

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Question 647305: the sum of the first fifteen terms of an arithmetic terms progression is 270. find the first term and the common difference if the the fifteenth terms is 39.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

the sum of the first fifteen terms of an arithmetic terms progression is 270. 

find the first term and the common difference if the the fifteenth terms is 39

S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2 ⇒ %2815%2F2%29%28a%5B1%5D+%2B+39%29+=+270, a%5B1%5D+=+36-39 = -3

a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad  ⇒ -3+%2B+14d+=+39⇒ 14d+=+42 d = 3

and

a%5B15%5D+=+-3+%2B+14%2A3+=+39