SOLUTION: If the sum of the arithmetic sequence is 17 the second term is 3 ,the d is 14 what is the first term

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Question 963769: If the sum of the arithmetic sequence is 17 the second term is 3 ,the d is 14 what is the first term
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
>>the sum of the arithmetic sequence is 17
`
>>the d is 14 
S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29
17=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22%2814%29%29
Multiply both sides by 2:
34=n%282a%5B1%5D%2B14%28n-1%29%5E%22%22%29
34=n%282a%5B1%5D%2B14n-14%29

>>the second term is 3,
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
3=a%5B1%5D%2B%282-1%29%2814%29
3=a%5B1%5D%2B%281%29%2814%29
3=a%5B1%5D%2B14
-11=a%5B1%5D

That's the answer, but the problem is botched because
when you substitute a1 = -11 into

34=n%282a%5B1%5D%2B14n-14%29

and solve for n you get:

n+=+%289+%2B-+10sqrt%282%29%29%2F7

So you might tell your teacher that the problem is botched.
There is no such arithmetic sequence because n can only
be a positive integer.

Edwin