document.write( "Question 1134805: Given the sequence:2;5;8;....
\n" ); document.write( "1. If the pattern continues ,then write down the next two terms.
\n" ); document.write( "2. Prove that none of the terms of this sequence are perfect squares. \n" ); document.write( "

Algebra.Com's Answer #752284 by ikleyn(52866) $\"\"$ $\"About$

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

\r\n" );
document.write( "Arithmetic sequence with the first term 2 and the common difference 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " = 2 + 3*(n-1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The next two terms are  11  and  14.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When divided by 3, every term gives the remainder of 2.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, neither term of this sequence is a square, because a square of an integer number NEVER gives remainder 2 when divided by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives the remainders 0 or 1, but never gives the remainder 2.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );