document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160078>Question 1160078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Find the 25th term of the arithmetic sequence\r<BR>\n" );
document.write( "\n" );
document.write( "‒7, ‒4, ‒1, 2, ...\r<BR>\n" );
document.write( "\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "2. In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.\r<BR>\n" );
document.write( "\n" );
document.write( "Then write the first four terms of the sequence.\r<BR>\n" );
document.write( "\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "3. In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an.\r<BR>\n" );
document.write( "\n" );
document.write( "Then write the first three terms of the sequence.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783221 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=783221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "These are straightforward problems involving arithmetic and geometric sequences; you can do the arithmetic....<br><BR>\n" );
document.write( "1. Find the 25th term of the arithmetic sequence  ‒7, ‒4, ‒1, 2, ...<br><BR>\n" );
document.write( "The common difference is +3<BR>\n" );
document.write( "The 25th term is the first term, plus the common difference 24 times<br><BR>\n" );
document.write( "2. In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.<BR>\n" );
document.write( "Then write the first four terms of the sequence.<br><BR>\n" );
document.write( "The difference between the 4th term and the 10th term is 30-18 = 12; that difference is 6 times the common difference.<BR>\n" );
document.write( "So you can easily find the common difference, d.<BR>\n" );
document.write( "Then the first term a1 is the 4th term, minus 3 times the common difference.<BR>\n" );
document.write( "Then the formula for an is the first term, plus (n-1) times the common difference.<br><BR>\n" );
document.write( "3. In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an.<BR>\n" );
document.write( "Then write the first three terms of the sequence.<br><BR>\n" );
document.write( "The 6th term, 40, is the 3rd term, (-5), multiplied by the common ratio 3 times:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40+=+%28-5%29%28r%5E3%29 ALIGN=MIDDLE  ALT=\"40+=+%28-5%29%28r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3+=+-8 ALIGN=MIDDLE  ALT=\"r%5E3+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-2 ALIGN=MIDDLE  ALT=\"r+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You have r; the first term a1 is the third term, -5, DIVIDED BY the common ratio two times; the formula for an is the first term, multiplied by the common ratio (n-1) times.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );