document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165459>Question 165459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you do arithmetic and geometric series ?\r<BR>\n" );
document.write( "\n" );
document.write( "Example <BR>\n" );
document.write( " <BR>\n" );
document.write( "2 + 10 + 18 + 26 +...;find S10 <BR>\n" );
document.write( " <BR>\n" );
document.write( "3 + 15 + 75 + 375 + ...; find S 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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 #121942 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you do arithmetic and geometric series ? <BR>\n" );
document.write( "Example \r<BR>\n" );
document.write( "\n" );
document.write( "2 + 10 + 18 + 26 +...;find S(10)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "There is a common difference of 10-2 = 8 between each pair of terms, so:<BR>\n" );
document.write( "d = 8; n=10, a(1) = 2<BR>\n" );
document.write( "Formul: <BR>\n" );
document.write( "S(n) = (n/2)(a+a(n)) where a(n) = a(1)+(n-1)d<BR>\n" );
document.write( "a(10) = 2 + (10-1)*8 = 2 + 72 = 74<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "S(10) = (10/2)(2+74) = 5*76 = 152<BR>\n" );
document.write( "--------------------------------------- \r<BR>\n" );
document.write( "\n" );
document.write( "3 + 15 + 75 + 375 + ...; find S(7)<BR>\n" );
document.write( "There is a common ratio of 15/3 = 5 between each pair of terms, so:<BR>\n" );
document.write( "r = 5; a(1) = 3<BR>\n" );
document.write( "s(7) = 3[(5^7-1)/(5-1)] = 58,593<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );