document.write( "Question 1111116: 2,12,36,80,150,? Series comoletion\n" ); document.write( " \n" ); document.write( "
\n" ); document.write( "n a_n diff diff_2 diff_3\n" ); document.write( "1 2 \n" ); document.write( "2 12 10\n" ); document.write( "3 36 24 14\n" ); document.write( "4 80 44 20 6 \n" ); document.write( "5 150 70 26 6 \r\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "Because the differences don't reach a constant for 3 levels, the form will be\r\n" ); document.write( "\n" ); document.write( "\r\n" ); document.write( "\n" ); document.write( "Using the first four values, you get these 4 equations:\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Which results in the following matrix equation:\r\n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "Which can be solved using matrix inversion to find:\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\r\n" ); document.write( "\n" ); document.write( "Therefore \r\n" ); document.write( "\n" ); document.write( "——\n" ); document.write( "Check:\n" ); document.write( " n=1: (ok)\n" ); document.write( " n=5: (ok)\r\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "