document.write( "Question 955505: if sn the sum of first n terms of an AP is given by Sn=3nsq-4n then find nth term
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #583813 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
\"S%5Bn%5D\" , the sum of first \"n\" terms of an AP (Arithmetic progression or Arithmetic sequence) , is given by
\n" ); document.write( "\"S%5Bn%5D=%282a%5B1%5D%2B%28n-1%29d%29%2An%2F2\" , where
\n" ); document.write( "\"a%5B1%5D\" is the first term, and
\n" ); document.write( "\"d\" is the common difference.
\n" ); document.write( "
\n" ); document.write( "The problem says that \"S%5Bn%5D=3n%5E2-4n\" (or so I guess),
\n" ); document.write( "and that is true for all and any natural number values of \"n\" .
\n" ); document.write( "So, we have to solve the equation
\n" ); document.write( "\"%282a%5B1%5D%2B%28n-1%29d%29%2An%2F2=3n%5E2-4n\" ,
\n" ); document.write( "which is true for all and any natural number values of \"n\" .
\n" ); document.write( "\"%282a%5B1%5D%2B%28n-1%29d%29%2An%2F2=3n%5E2-4n\"<-->\"%282a%5B1%5Dn%2Bdn%5E2-dn%29%2F2=3n%5E2-4n\"<-->\"%28dn%5E2%2B2a%5B1%5Dn-dn%29%2F2=3n%5E2-4n\"<-->\"%28d%2F2%29n%5E2%2B%28%282a%5B1%5D-d%29%2F2%29n=3n%5E2-4n\"
\n" ); document.write( "If that must be true for all and any natural number values of \"n\" ,
\n" ); document.write( "then the coefficients of the terms in \"n%5E2\" and \"n\" must be the same, so
\n" ); document.write( "\"system%28d%2F2=3%2C%282a%5B1%5D-d%29%2F2=-4%29\"-->\"system%28d=6%2C%282a%5B1%5D-6%29%2F2=-4%29\"-->\"system%28d=6%2Ca%5B1%5D-3=-4%29\"-->\"system%28d=6%2Ca%5B1%5D=-1%29\" .
\n" ); document.write( "For any AP, the nth term is given by
\n" ); document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\" , where
\n" ); document.write( "\"a%5B1%5D\" is the first term, and
\n" ); document.write( "\"d\" is the common difference.
\n" ); document.write( "With \"system%28d=6%2Ca%5B1%5D=-1%29\" , \"a%5Bn%5D=-1%2B6%28n-1%29\"<-->\"a%5Bn%5D=6n-7\" \n" ); document.write( "
\n" );