document.write( "Question 1118377: What are the first three terms if the 11th term of an
\n" );
document.write( "arithmetic sequence is 60 and the sum of the first 11
\n" );
document.write( "terms is 55?
\n" );
document.write( " \n" );
document.write( "
Algebra.Com's Answer #733675 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! What are the first three terms if the 11th term of an \n" ); document.write( "arithmetic sequence is 60 and the sum of the first 11 \n" ); document.write( "terms is 55? \n" ); document.write( " \r\n" ); document.write( "a1,__,__,__,__,__,__,__,__,__,60,...\r\n" ); document.write( "\r\n" ); document.write( "Sn = (n/2)(a1 + an)\r\n" ); document.write( "\r\n" ); document.write( "S11 = (11/2)(a1 + a11)\r\n" ); document.write( "\r\n" ); document.write( "55 = (11/2)(a1 + 60)\r\n" ); document.write( "\r\n" ); document.write( "Multiply both sides by 2\r\n" ); document.write( "\r\n" ); document.write( "110 = 11(a1 + 60)\r\n" ); document.write( "\r\n" ); document.write( "110 = 11a1 + 660\r\n" ); document.write( "\r\n" ); document.write( "-550 = 11a1\r\n" ); document.write( "\r\n" ); document.write( "-550/11 = a1\r\n" ); document.write( "\r\n" ); document.write( "-50 = a1 \r\n" ); document.write( "\r\n" ); document.write( "So\r\n" ); document.write( "\r\n" ); document.write( "a1,__,__,__,__,__,__,__,__,__,60,\r\n" ); document.write( "\r\n" ); document.write( "becomes\r\n" ); document.write( "\r\n" ); document.write( "-50,__,__,__,__,__,__,__,__,__,60,\r\n" ); document.write( "\r\n" ); document.write( "To fill in the blanks, we only need the common difference d:\r\n" ); document.write( "\r\n" ); document.write( "an = a1 + (n - 1)d\r\n" ); document.write( "\r\n" ); document.write( " 60 = -50 + (11 - 1)d\r\n" ); document.write( " 60 = -50 + 10d\r\n" ); document.write( "110 = 10d\r\n" ); document.write( " 11 = d\r\n" ); document.write( "\r\n" ); document.write( "So the sequence\r\n" ); document.write( "\r\n" ); document.write( "-50,__,__,__,__,__,__,__,__,__,60,...\r\n" ); document.write( "\r\n" ); document.write( "becomes\r\n" ); document.write( "\r\n" ); document.write( "-50,-39,-28,-17,-6,5,16,27,38,49,60,...\r\n" ); document.write( "\r\n" ); document.write( "So the first three terms are -50,-39 and -28\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |