document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=489968>Question 489968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm a high school student in Algebra 2. I have a couple questions, <BR>\n" );
document.write( "1. what are the formulas to find the nth term of an arithmetic and geometric sequence? here is a problem im having trouble with..<BR>\n" );
document.write( "write a formula for the nth term of an arithmetic sequence, then a25. <BR>\n" );
document.write( "d=2 a12=18<BR>\n" );
document.write( "an=_____<BR>\n" );
document.write( "a25=_____<BR>\n" );
document.write( "I'm not really confident on how to find the answer :( \r<BR>\n" );
document.write( "\n" );
document.write( "Another question I have is how to find the sum..<BR>\n" );
document.write( "ex. find the sum of the first n terms when n=20. <BR>\n" );
document.write( "arithmetic series: 40+37++34+31+....\r<BR>\n" );
document.write( "\n" );
document.write( "then im supposed to find n for Sn=195, how do i do that??\r<BR>\n" );
document.write( "\n" );
document.write( "thanks for the help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333828 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=333828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. what are the formulas to find the nth term of an arithmetic and geometric sequence? here is a problem im having trouble with..<BR>\n" );
document.write( "write a formula for the nth term of an arithmetic sequence<BR>\n" );
document.write( "a(n) , then a25. <BR>\n" );
document.write( "when d=2 and a(12) = 18<BR>\n" );
document.write( "Ans: an=a(1)+(n-1)d<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Since a(12) = a(1)+11*2 = 18<BR>\n" );
document.write( "a(1) = 18 - 22 = -4<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Ans: a25= a(1)+24d<BR>\n" );
document.write( "a(25) = -4+24*2<BR>\n" );
document.write( "a(25) = 44<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Another question I have is how to find the sum..<BR>\n" );
document.write( "ex. find the sum of the first n terms when n=20. <BR>\n" );
document.write( "arithmetic series: 40+37+34+31+....<BR>\n" );
document.write( "--<BR>\n" );
document.write( "S(n) = (n/2)[(a(1)+a(n)]<BR>\n" );
document.write( "a(1) = 40<BR>\n" );
document.write( "d = -3<BR>\n" );
document.write( "a(n) = a(20) = 40+(19)*-3 = -17<BR>\n" );
document.write( "----<BR>\n" );
document.write( "S(20) = (20/2)[40-17] = 10[23] = 230<BR>\n" );
document.write( "========================================<BR>\n" );
document.write( " <BR>\n" );
document.write( "then im supposed to find n for S(n)=195, how do i do that??<BR>\n" );
document.write( "a(n) = 40 + (n-1)(-3) = 40-3n+3 = 43-3n<BR>\n" );
document.write( "Solve: (n/2)(40 + 43-3n) = 195<BR>\n" );
document.write( "(n/2)(83-3n) = 195<BR>\n" );
document.write( "n(83-3n) = 390<BR>\n" );
document.write( "-3n^2 + 82n - 390 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve for \"n\":<BR>\n" );
document.write( "Use the quadratic formula to get the whole number answer.<BR>\n" );
document.write( "Ans: n = 6<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );