document.write( "Question 558951: Try to solve this sequence
\n" ); document.write( "112 , 2112 , 2122 ....
\n" ); document.write( "Calculate the further terms \n" ); document.write( "
Algebra.Com's Answer #363287 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "t1 = 112\r\n" );
document.write( "t2 = 2112\r\n" );
document.write( "t3 = 2122\r\n" );
document.write( "\r\n" );
document.write( "Three terms always determine a quadratic sequence.\r\n" );
document.write( "\r\n" );
document.write( "So let the nth term be \r\n" );
document.write( "\r\n" );
document.write( "tn = an² + bn + c\r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "t1 = 112 = a(1)² + b(1) + c \r\n" );
document.write( "\r\n" );
document.write( "                          a + b + c =  112\r\n" );
document.write( "\r\n" );
document.write( "t2 = 2112 = a(2)² + b(2) + c \r\n" );
document.write( "\r\n" );
document.write( "                         4a + 2b + c = 2112\r\n" );
document.write( "\r\n" );
document.write( "t3 = 2122 = a(3)² + b(3) + c \r\n" );
document.write( "\r\n" );
document.write( "                         9a + 3b + c = 2122\r\n" );
document.write( "\r\n" );
document.write( " So we solve the system:\r\n" );
document.write( "\r\n" );
document.write( "ì a +  b + c =   112\r\n" );
document.write( "í4a + 2b + c =  2112\r\n" );
document.write( "î9a + 3b + c =  2122\r\n" );
document.write( "\r\n" );
document.write( "We get a=-995, b = 4985, and c = -3878\r\n" );
document.write( "\r\n" );
document.write( "So the three terms given fit the sequence:\r\n" );
document.write( "\r\n" );
document.write( "tn = -995n² + 4985t - 3878\r\n" );
document.write( "\r\n" );
document.write( "So the first 50 terms are:\r\n" );
document.write( "\r\n" );
document.write( "t1 = -995(1)² + 4985(1) - 3878 = 112\r\n" );
document.write( "t2 = -995(2)² + 4985(2) - 3878 = 2112\r\n" );
document.write( "t3 = -995(3)² + 4985(3) - 3878 = 2122\r\n" );
document.write( "t4 = -995(4)² + 4985(4) - 3878 = 142\r\n" );
document.write( "t5 = -995(5)² + 4985(5) - 3878 = -3828\r\n" );
document.write( "t6 = -995(6)² + 4985(6) - 3878 = -9788\r\n" );
document.write( "t7 = -995(7)² + 4985(7) - 3878 = -17738\r\n" );
document.write( "t8 = -995(8)² + 4985(8) - 3878 = -27678\r\n" );
document.write( "t9 = -995(9)² + 4985(9) - 3878 = -39608\r\n" );
document.write( "t10 = -995(10)² + 4985(10) - 3878 = -53528\r\n" );
document.write( "t11 = -995(11)² + 4985(11) - 3878 = -69438\r\n" );
document.write( "t12 = -995(12)² + 4985(12) - 3878 = -87338\r\n" );
document.write( "t13 = -995(13)² + 4985(13) - 3878 = -107228\r\n" );
document.write( "t14 = -995(14)² + 4985(14) - 3878 = -129108\r\n" );
document.write( "t15 = -995(15)² + 4985(15) - 3878 = -152978\r\n" );
document.write( "t16 = -995(16)² + 4985(16) - 3878 = -178838\r\n" );
document.write( "t17 = -995(17)² + 4985(17) - 3878 = -206688\r\n" );
document.write( "t18 = -995(18)² + 4985(18) - 3878 = -236528\r\n" );
document.write( "t19 = -995(19)² + 4985(19) - 3878 = -268358\r\n" );
document.write( "t20 = -995(20)² + 4985(20) - 3878 = -302178\r\n" );
document.write( "t21 = -995(21)² + 4985(21) - 3878 = -337988\r\n" );
document.write( "t22 = -995(22)² + 4985(22) - 3878 = -375788\r\n" );
document.write( "t23 = -995(23)² + 4985(23) - 3878 = -415578\r\n" );
document.write( "t24 = -995(24)² + 4985(24) - 3878 = -457358\r\n" );
document.write( "t25 = -995(25)² + 4985(25) - 3878 = -501128\r\n" );
document.write( "t26 = -995(26)² + 4985(26) - 3878 = -546888\r\n" );
document.write( "t27 = -995(27)² + 4985(27) - 3878 = -594638\r\n" );
document.write( "t28 = -995(28)² + 4985(28) - 3878 = -644378\r\n" );
document.write( "t29 = -995(29)² + 4985(29) - 3878 = -696108\r\n" );
document.write( "t30 = -995(30)² + 4985(30) - 3878 = -749828\r\n" );
document.write( "t31 = -995(31)² + 4985(31) - 3878 = -805538\r\n" );
document.write( "t32 = -995(32)² + 4985(32) - 3878 = -863238\r\n" );
document.write( "t33 = -995(33)² + 4985(33) - 3878 = -922928\r\n" );
document.write( "t34 = -995(34)² + 4985(34) - 3878 = -984608\r\n" );
document.write( "t35 = -995(35)² + 4985(35) - 3878 = -1048278\r\n" );
document.write( "t36 = -995(36)² + 4985(36) - 3878 = -1113938\r\n" );
document.write( "t37 = -995(37)² + 4985(37) - 3878 = -1181588\r\n" );
document.write( "t38 = -995(38)² + 4985(38) - 3878 = -1251228\r\n" );
document.write( "t39 = -995(39)² + 4985(39) - 3878 = -1322858\r\n" );
document.write( "t40 = -995(40)² + 4985(40) - 3878 = -1396478\r\n" );
document.write( "t41 = -995(41)² + 4985(41) - 3878 = -1472088\r\n" );
document.write( "t42 = -995(42)² + 4985(42) - 3878 = -1549688\r\n" );
document.write( "t43 = -995(43)² + 4985(43) - 3878 = -1629278\r\n" );
document.write( "t44 = -995(44)² + 4985(44) - 3878 = -1710858\r\n" );
document.write( "t45 = -995(45)² + 4985(45) - 3878 = -1794428\r\n" );
document.write( "t46 = -995(46)² + 4985(46) - 3878 = -1879988\r\n" );
document.write( "t47 = -995(47)² + 4985(47) - 3878 = -1967538\r\n" );
document.write( "t48 = -995(48)² + 4985(48) - 3878 = -2057078\r\n" );
document.write( "t49 = -995(49)² + 4985(49) - 3878 = -2148608\r\n" );
document.write( "t50 = -995(50)² + 4985(50) - 3878 = -2242128\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );