![\"\"](\"/images/stars/stars-12.gif\")
You can put this solution on YOUR website!
Call the first term x and the second term y.
\n" );
document.write( "1: x
\n" );
document.write( "2: y
\n" );
document.write( "3: x+y
\n" );
document.write( "4: x+y + y = x+2y (added the previous two terms).
\n" );
document.write( "5: 2x+3y
\n" );
document.write( "6: 3x+5y
\n" );
document.write( "7: 5x+8y
\n" );
document.write( "8: 8x + 13y = 390
\n" );
document.write( "9: 13x+21y
\n" );
document.write( "The problem states that the second term, y, is greater than the first term, x. They are both positive and both integers.
\n" );
document.write( "Try a few: y = x+1 gives term 8 as:
\n" );
document.write( "8x + 13(x+1) = 390
\n" );
document.write( "8x + 13x + 13 = 390
\n" );
document.write( "21x = 377
\n" );
document.write( "x = 377/21 which is not an integer. So y cannot be x+1.
\n" );
document.write( "Try y = x+2:
\n" );
document.write( "8x + 13(x+2) = 390
\n" );
document.write( "8x +13x +26 = 390
\n" );
document.write( "21x = 364
\n" );
document.write( "364/21 = not an integer.
\n" );
document.write( "Now there's a pattern. In each case (y+n), x= (390-13n)/21. It must be an integer.
\n" );
document.write( "n = 3, 4, 5, 6, 7, 8 don't work. But n=9 works.
\n" );
document.write( "8x + 13(x+9)= 390
\n" );
document.write( "8x+13x + 117 = 390
\n" );
document.write( "21x = 273
\n" );
document.write( "x = 273/21 = (390-13*9)/21 = 13.
\n" );
document.write( "x = 13 and y = 13+9 = 22
\n" );
document.write( "The 9th term is 13x + 21y = 13(13)+21(22) = 169 + 462 = 631
\n" );
document.write( "
Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
\n" ); document.write( "