document.write( "Question 993264: Determine the number of terms in an arthmetic
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Algebra.Com's Answer #612554 by Edwin McCravy(20056)\"\" \"About 
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Determine the number of terms in an arthmetic
\n" ); document.write( "sequence with t3= -17.5 and t10= -52.5. the
\n" ); document.write( "final term in the sequence is -147.5
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document.write( "\"t%5Bn%5D\"\"%22%22=%22%22\"\"t%5B1%5D%2B%28n-1%29d\"\r\n" );
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document.write( "Substitute n=3 and t3=-17.5\r\n" );
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document.write( "\"t%5B3%5D\"\"%22%22=%22%22\"\"t%5B1%5D%2B%283-1%29d\"\r\n" );
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document.write( "\"-17.5\"\"%22%22=%22%22\"\"t%5B1%5D%2B2d\"\r\n" );
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document.write( "Substitute n=10 and t10=-52.5\r\n" );
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document.write( "\"t%5B10%5D\"\"%22%22=%22%22\"\"t%5B1%5D%2B%2810-1%29d\"\r\n" );
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document.write( "\"-52.5\"\"%22%22=%22%22\"\"t%5B1%5D%2B9d\"\r\n" );
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document.write( "Now we have a system of equations:\r\n" );
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document.write( "\"system%28t%5B1%5D%2B2d-17.5%2Ct%5B1%5D%2B9d=-52.5%29\"\r\n" );
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document.write( "Solve that system and get t1=-7.5, d=-5\r\n" );
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document.write( "the final term in the sequence is -147.5\r\n" );
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document.write( "Substitute t1=-7.5, d=-5 and tn=-52.5\r\n" );
document.write( "in the same formula\r\n" );
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document.write( "\"-52.5\"\"%22%22=%22%22\"\"-7.5%2B%28n-1%29%28-5%29\"\r\n" );
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document.write( "Solve that and get n = 10\r\n" );
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document.write( "Edwin
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