document.write( "Question 898992: In an arithmetic series, the 'pth' term is q and the 'qth' term is p , find the 'mth' term. \r
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Algebra.Com's Answer #545090 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
'pth' term is q and the 'qth' term is p
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\" <-- general term\r\n" );
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document.write( "\"q=a%5Bp%5D=a%5B1%5D%2B%28p-1%29d\" and \"p=a%5Bq%5D=a%5B1%5D%2B%28q-1%29d\"\r\n" );
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document.write( "We solve the system:\r\n" );
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document.write( "\"system%28a%5B1%5D%2B%28p-1%29d=q%2C+a%5B1%5D%2B%28q-1%29d=p%29\"\r\n" );
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document.write( "Eliminate a1 by subtracting the equations:\r\n" );
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document.write( "(p-1)d-(q-1)d = q-p\r\n" );
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document.write( "d[(p-1)-(q-1)] = q-p\r\n" );
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document.write( "d[p-1-q+1] = q-p\r\n" );
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document.write( "d(p-q) = q-p\r\n" );
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document.write( "d = \"%28q-p%29%2F%28p-q%29\"\r\n" );
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document.write( "d = \"%28-p%2Bq%29%2F%28p-q%29\"\r\n" );
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document.write( "d = \"%28-1%28p-q%29%29%2F%28p-q%29\"\r\n" );
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document.write( "d = -1\r\n" );
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document.write( "Substitute d = -1\r\n" );
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document.write( "\"a%5B1%5D%2B%28p-1%29d=q\"\r\n" );
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document.write( "\"a%5B1%5D%2B%28p-1%29%28-1%29=q\"\r\n" );
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document.write( "\"a%5B1%5D-p%2B1=q\"\r\n" );
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document.write( "\"a%5B1%5D=p%2Bq-1\"\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\" <-- general term\r\n" );
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document.write( "Substitute a1 = p+q-1, d = -1, and n = m\r\n" );
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document.write( "\"a%5Bm%5D=%28p%2Bq-1%29%2B%28m-1%29%28-1%29\"\r\n" );
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document.write( "\"a%5Bm%5D=p%2Bq-1%2B%28-m%2B1%29\"\r\n" );
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document.write( "\"a%5Bm%5D=p%2Bq-1-m%2B1\"\r\n" );
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document.write( "\"a%5Bm%5D=p%2Bq-m\"\r\n" );
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document.write( "Edwin
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