document.write( "Question 190402: Write the next term in the sequence. Then write a rule for the nth term.
\n" ); document.write( " -5, 10, -15, 20,... \n" ); document.write( "

Algebra.Com's Answer #142900 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
Write the next term in the sequence.
\n" ); document.write( "Then write a rule for the nth term.\r
\n" ); document.write( "\n" ); document.write( "-5, 10, -15, 20, ...
\n" ); document.write( "

\r\n" );
document.write( "If it weren't for the signs,\r\n" );
document.write( "we would have the sequence \r\n" );
document.write( "\r\n" );
document.write( "5, 10, 15, 20, ...\r\n" );
document.write( "\r\n" );
document.write( "So let's first get the nth term of that sequence.\r\n" );
document.write( "The difference between any term and the preceding\r\n" );
document.write( "term is 5. So the common difference d = 5.  The\r\n" );
document.write( "nth term of an arithmetic sequence is given by:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "Substituting,\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we have to tack on a factor that\r\n" );
document.write( "will cause the signs to alternate:\r\n" );
document.write( "\r\n" );
document.write( "The alternating sign factors are \r\n" );
document.write( "and , depending on whether\r\n" );
document.write( "the first term is negative or positive. Since \r\n" );
document.write( "the first term is -5, a negative number, we\r\n" );
document.write( "use  for the alternating sign\r\n" );
document.write( "factor.  So if we use (capital \"A\")  \r\n" );
document.write( "for the nth term, we just multiply the nth term\r\n" );
document.write( "for  (small \"a\") above by  \r\n" );
document.write( "and get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );