document.write( "Question 978276: Given a4=35 and s14=931, find the common difference d and a1. \n" ); document.write( "
Algebra.Com's Answer #599780 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
[You did not give enough information.  You had this:
an=35 and s14=931 a sub n ,common diffence and a sub 1
However I guessed that a4=35 was given, and rewrote your question as above.]\r\n" );
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document.write( "We use the nth term formula:\r\n" );
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document.write( "\"a%5Bn%5D\"\"%22%22=%22%22\"\"a%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "Substitute n=4, then a4=35\r\n" );
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document.write( "\"a%5B4%5D\"\"%22%22=%22%22\"\"a%5B1%5D%2B%284-1%29d\"\r\n" );
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document.write( "\"35\"\"%22%22=%22%22\"\"a%5B1%5D%2B3d\"\r\n" );
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document.write( "We use the sum formula:\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%5E%22%22%29\"\r\n" );
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document.write( "Substitute n=14, then S14=931\r\n" );
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document.write( "\"S%5B14%5D\"\"%22%22=%22%22\"\"expr%2814%2F2%29%282a%5B1%5D%2B%2814-1%29d%5E%22%22%29\"\r\n" );
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document.write( "\"931\"\"%22%22=%22%22\"\"7%282a%5B1%5D%2B13d%5E%22%22%29\"\r\n" );
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document.write( "Both sides can be divided through by 7:\r\n" );
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document.write( "\"133\"\"%22%22=%22%22\"\"2a%5B1%5D%2B13d%5E%22%22%29\"\r\n" );
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document.write( "So now we have this system of equations:\r\n" );
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document.write( "\"system%2835=a%5B1%5D%2B3d%2C133=2a%5B1%5D%2B13d%29\"\r\n" );
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document.write( "Solve that and get a1=8, d=8.\r\n" );
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document.write( "If my guess of a4=35 is correct, then your sequence was\r\n" );
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document.write( "8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 98, 107, 116, 125 \r\n" );
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document.write( "That sequence of 14 terms does have sum 931.\r\n" );
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document.write( "If I guessed wrong, then you can use the above as a guide.\r\n" );
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document.write( "Edwin
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