SOLUTION: The difference between the tenth term and the seventh term of an arithmetic sequence is -60. The twelfth term divided by the sixth term is 2. Find the first term and the common dif

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Question 1036199: The difference between the tenth term and the seventh term of an arithmetic sequence is -60. The twelfth term divided by the sixth term is 2. Find the first term and the common difference.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the given, a%5B10%5D+-+a%5B7%5D+=+-60 and a%5B12%5D%2Fa%5B6%5D+=+2.
The first equation becomes a%5B1%5D+%2B9d+-+%28a%5B1%5D%2B6d%29+=+-60 ==> 3d = -60 ==> d = -20.
The second equation becomes a%5B12%5D+=+2a%5B6%5D.
==> a%5B1%5D+%2B+11%2A-20+=+2%28a%5B1%5D+%2B+5%2A-20%29
<==> a%5B1%5D+-+220+=+2a%5B1%5D+-+200
==> a%5B1%5D+=+-20