document.write( "Question 956360: How to find An and n if Sn,A1 and d is given? \n" ); document.write( "
Algebra.Com's Answer #584342 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Start with this sum formula for an arithmetic sequence:\r\n" );
document.write( "\r\n" );
document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute Sn, a1 and d in this formula\r\n" );
document.write( "and solve.  It should factor if there is a solution.  \r\n" );
document.write( "\r\n" );
document.write( "Using the letters and the quadratic formula, I got this:\r\n" );
document.write( "\r\n" );
document.write( "\"n+=+%28d-a%5B1%5D+%2B-+sqrt%28%28a%5B1%5D-d%29%5E2%2B8dS%5Bn%5D%29%29%2F%282d%29\"\r\n" );
document.write( "\r\n" );
document.write( "At least one of those two solutions (using either the + or the -) \r\n" );
document.write( "will give a positive whole number for n, if there is a solution.\r\n" );
document.write( "\r\n" );
document.write( "Then substitute that value of n along with a1 and d\r\n" );
document.write( "into the general term formula:\r\n" );
document.write( "\r\n" );
document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"  \r\n" );
document.write( "\r\n" );
document.write( "In some cases there may be two solutions.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );