document.write( "Question 1161033: If a sequence is defined recursively by f(1)= -2 and f(n-1) = 3(n-1)-4, then find the first 4 terms of the sequence? \n" ); document.write( "
Algebra.Com's Answer #784449 by ikleyn(52790)![]() ![]() You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " The problem formulation, strictly saying, is incomplete, since it DOES NOT define for which values of \"n\" the given formula is valid.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " But if we assume that it is valid for any integer n >= 3, then see my solution below.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " Read it VERY ATTENTIVELY.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " Also notice that the formula is INVALID for n= 2.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Solution\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "It is INCORRECT to call this formula recursive.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "There is NO recursion in it.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "It is an EXPLICIT formula f(m) = 3m-4, for any integer m >= 2, if we accept my assumption above.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "So, f(2) = 3*2 - 4 = 6 - 4 = 2;\r\n" ); document.write( "\r\n" ); document.write( " f(3) = 3*3 - 4 = 9 - 4 = 5;\r\n" ); document.write( "\r\n" ); document.write( " f(4) = 3*4 - 4 = 12 - 4 = 8.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "You can easily calculate million next terms in this way, if you want.\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( "--------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Very important POST-NOTE :\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " It is a GROSS MISTAKE to call this formula recursive (!)\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |