document.write( "Question 479925: how do you find the recursive formula and the indicated term of this sequence 1,5,14,30,55,91? \n" ); document.write( "
Algebra.Com's Answer #328779 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! 1,5,14,30,55,91 \n" ); document.write( " \r\n" ); document.write( "Notice that:\r\n" ); document.write( "\r\n" ); document.write( "to get from 1 to 5 you have to add 4, then\r\n" ); document.write( "to get from 4 to 14 you have to add 9, then\r\n" ); document.write( "to get from 14 to 30 you have to add 16, then\r\n" ); document.write( "to get from 30 to 55 you have to add 25, then\r\n" ); document.write( "to get from 55 to 91 you have to add 36.\r\n" ); document.write( "\r\n" ); document.write( "Notice that we are always adding perfect squares. So,\r\n" ); document.write( "if we wanted the next term, we'd just add 91 plus\r\n" ); document.write( "the next perfect square 49, and get 91 + 49 = 140.\r\n" ); document.write( "\r\n" ); document.write( "We start with the first term of 1, \r\n" ); document.write( "then we add 2² to the 1st term to get the 2nd term,\r\n" ); document.write( "then we add 3² to the 2nd term to get the 3rd term,\r\n" ); document.write( "then we add 4² to the 3rd term to get the 4th term,\r\n" ); document.write( "then we add 5² to the 4th term to get the 5th term,\r\n" ); document.write( "then we add 6² to the 5th term to get the 6th term,\r\n" ); document.write( "\r\n" ); document.write( "So the recusive formula is just a rule that\r\n" ); document.write( "tells what we start with, a1, and what we do each time\r\n" ); document.write( "to get the next term, an+1, from the preceding term.\r\n" ); document.write( "So the recursion formula is:\r\n" ); document.write( "\r\n" ); document.write( "a1=1. an+1=an+(n+1)², for n≧1.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |