document.write( "Question 1161108: The sequence 2, 3, 5, 6, 7, 10, ... consists of all counting numbers which are neither perfect squares nor perfect cubes. Find the 75th term of this sequence. \n" ); document.write( "

Algebra.Com's Answer #784580 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Write all consecutive integer numbers 1, 2, 3, 4, 5 and so on, until, let say, 100.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this sequence, erase perfect cubes and perfect squares\r\n" );
document.write( "\r\n" );
document.write( "    1, 4, 8, 9, 16, 25, 27, 36, 49, 64, 81, 100.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In all, you will erase 12 terms;  11 of them are less than or equal to 81.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now you can easily understand that the 75-th term of your sequence is the number 86,  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   +----------------------------------------------------------------------------+\r\n" );
document.write( "   |   because 86 original terms  MINUS  11 erased terms = 75 remaining terms.  |\r\n" );
document.write( "   +----------------------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The 75-th term of your sequence is the number 86.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is a good problem for 4-th - 5-th grade kids, of the Math circle or Math Olympiad level \r
\n" ); document.write( "\n" ); document.write( "at a school or local University.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "First, it teaches to think;\r
\n" ); document.write( "\n" ); document.write( "second, it teaches on how to find an idea;\r
\n" ); document.write( "\n" ); document.write( "third, it teaches to organize your thoughts;\r
\n" ); document.write( "\n" ); document.write( "fourth, it teaches to EXPRESS your thoughts;\r
\n" ); document.write( "\n" ); document.write( "fifth, it teaches that even Math problem, which seems to be tedious, can be solved and made as sweet as a cookie (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Come again to the forum soon to learn something new from me (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Bring nice problems with you (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );