document.write( "Question 1036737: In an arithmetic progression, the thirteenth term
\n" ); document.write( "Is 27, and the seven term is three times the second term.find the first term and the common differences. \n" ); document.write( "

Algebra.Com's Answer #651541 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In an arithmetic progression, the thirteenth term
\n" ); document.write( "is 27, and the $\"highlight%28cross%28seven%29%29\"$ seventh term is three times the second term.
\n" ); document.write( "Find the first term and the common differences.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "We are given \r\n" );
document.write( "\r\n" );
document.write( " = 27,         (1)\r\n" );
document.write( "  = .      (2)\r\n" );
document.write( "\r\n" );
document.write( "which, in other terms, is\r\n" );
document.write( "\r\n" );
document.write( " + 12*d = 27,           (1')\r\n" );
document.write( " +  6*d = .   (2').\r\n" );
document.write( "\r\n" );
document.write( "Simplify it and write in the canonical form for the system of two equations in two unknowns:\r\n" );
document.write( "\r\n" );
document.write( "   + 12*d = 27,         (1'')\r\n" );
document.write( " +  3*d =  0.         (2'')\r\n" );
document.write( "\r\n" );
document.write( "Now, based on (2''), replace the term 12*d in (1'') by . You will get a single equation for \r\n" );
document.write( "\r\n" );
document.write( " = 27,   or    = 27,  which gives you   = 3.\r\n" );
document.write( "\r\n" );
document.write( "Then from (2'')  3d =  = 6.  Hence,  d = 2.\r\n" );
document.write( "\r\n" );
document.write( "Answer.   = 3,  d = 2.\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );