document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208031>Question 208031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Id have a question how would I find the sum of the first 20 terms od the series; 1+8+64+512....<BR>\n" );
document.write( "I know that its always times 8; example: 512*8=4096 and then 4096*8...ect. but I bet there is an easier way to find the answer (I mean other than going through all numbers like that) <BR>\n" );
document.write( "If possible could soemone tell me if 1.64703073*10^17 is the sum of the first 20 terms??  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157343 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Id have a question how would I find the sum of the first 20 terms od the series; 1+8+64+512....<BR>\n" );
document.write( "I know that its always times 8; example: 512*8=4096 and then 4096*8...ect. but I bet there is an easier way to find the answer (I mean other than going through all numbers like that) <BR>\n" );
document.write( "If possible could soemone tell me if 1.64703073*10^17 is the sum of the first 20 terms??<BR>\n" );
document.write( "----- <BR>\n" );
document.write( "1 = 8^0<BR>\n" );
document.write( "8 = 8^1<BR>\n" );
document.write( "64 = 8^2<BR>\n" );
document.write( "512 = 8^3<BR>\n" );
document.write( "4096 = 8^4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the 5th term is 8^4, this means that the 20th term would be 8^19 otherwise known as 8^(n-1)<BR>\n" );
document.write( "n = 20, (n-1) = 19<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that doesn't solve for our sum though.<BR>\n" );
document.write( "here you're in luck because there is a formula for finding the sum of a geometric series.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "i found this one at: <BR>\n" );
document.write( "http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_GeoSeries.xml<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the formula is:<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Sn = a1 * (1 - r^n) / (1 - r)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Sn = Sum of the first n terms in the sequence.<BR>\n" );
document.write( "a1 is the first term in the sequence.<BR>\n" );
document.write( "n is the number of terms in the sequence.<BR>\n" );
document.write( "r is the common ratio<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's see how it works.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your first 5 numbers in your geometric sequence are:<BR>\n" );
document.write( "1<BR>\n" );
document.write( "8<BR>\n" );
document.write( "64<BR>\n" );
document.write( "512<BR>\n" );
document.write( "4096<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this sum should be: 4681<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's see if it works.<BR>\n" );
document.write( "Sn = a1 * (1 - r^n) / (1 - r)<BR>\n" );
document.write( "a1 = 1<BR>\n" );
document.write( "r = 8<BR>\n" );
document.write( "n = 5<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "Sn = 1 * (1 - 8^5) / (1 - 8)<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "Sn = 1 * (-32767) / -7 = 4681<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "it works !!!!!<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using this on the full geometric series you have, we get:<BR>\n" );
document.write( "Sn = a1 * (1 - r^n) / (1 - r)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a1 = 1<BR>\n" );
document.write( "r = 8<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "Sn = 1 * (1 - 8^20) / (1 - 8)<BR>\n" );
document.write( "= 1 * (1.152922 * 10^18) / (-7)<BR>\n" );
document.write( "= 1.647031 * 10^17<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is pretty close to the answer you got, if not right on.<BR>\n" );
document.write( "i did it in excel to carry the answer out a few more digits.<BR>\n" );
document.write( "this is what i got:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "1.64703072086692E+17<BR>\n" );
document.write( "this number is the same as:<BR>\n" );
document.write( "164703072086692000.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );