document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52438>Question 52438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:<BR>\n" );
document.write( "a) 	What is r, the ratio between 2 consecutive terms? <BR>\n" );
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document.write( "b) 	Using the formula for the nth term of a geometric sequence, what is the 24th term?<BR>\n" );
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document.write( "c) 	Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34972 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK<BR>\n" );
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document.write( "    Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:<BR>\n" );
document.write( "a)   What is r, the ratio between 2 consecutive terms? <BR>\n" );
document.write( "Answer:<BR>\n" );
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document.write( "r = 2\r<BR>\n" );
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document.write( "b)   Using the formula for the nth term of a geometric sequence, what is the 24th term?<BR>\n" );
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document.write( "      a24 = 8388608<BR>\n" );
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document.write( "an = 2n-1<BR>\n" );
document.write( "a24 = 224-1<BR>\n" );
document.write( "a24 = 223<BR>\n" );
document.write( "a24 = 8388608  \r<BR>\n" );
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document.write( "c)   Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? <BR>\n" );
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document.write( "Sum a10 = 1023\r<BR>\n" );
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document.write( "Sum an = (2n - 1) / ( 2 - 1 )<BR>\n" );
document.write( "Sum a10 = ( 210 - 1 ) / ( 2 - 1 )<BR>\n" );
document.write( "      Sum a10 = ( 210 - 1 ) / ( 1 )<BR>\n" );
document.write( "Sum a10 = ( 1024 - 1 ) / ( 1 )<BR>\n" );
document.write( "Sum a10 = ( 1023 ) / ( 1 )<BR>\n" );
document.write( "Sum a10 = 1023<BR>\n" );
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document.write( "3)         Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:<BR>\n" );
document.write( "a)   What is r, the ratio between 2 consecutive terms? <BR>\n" );
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document.write( "r = 1/2<BR>\n" );
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document.write( "b)   Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.<BR>\n" );
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document.write( "a9 = 1.9980\r<BR>\n" );
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document.write( "Sum an = (.5n+1 - 1) / ( .5 - 1 )<BR>\n" );
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document.write( "            Starts at 0 so a9 is 10 terms.<BR>\n" );
document.write( "Sum a9 = (.59+1 - 1) / ( .5 - 1 )<BR>\n" );
document.write( "Sum a9 = (.00195 - 1) / ( -.5 )<BR>\n" );
document.write( "Sum a9 = (-.99002) / ( -.5 )<BR>\n" );
document.write( "a9 = 1.9980<BR>\n" );
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document.write( "c)   Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.<BR>\n" );
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document.write( "a10 = 1.9995<BR>\n" );
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document.write( "Sum an = (.5n+1 - 1) / ( .5 - 1 )<BR>\n" );
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document.write( "            Starts at 0 so a11 is 12 terms.<BR>\n" );
document.write( "Sum a11 = (.511+1 - 1) / ( .5 - 1 )<BR>\n" );
document.write( "Sum a11 = (.000244 - 1) / ( -.5 )<BR>\n" );
document.write( "Sum a11 = (-.99976) / ( -.5 )<BR>\n" );
document.write( "a9 = 1.9980<BR>\n" );
document.write( "a10 = 1.9995\r<BR>\n" );
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document.write( "d)   What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?<BR>\n" );
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document.write( "The Sum is always smaller than 2.<BR>\n" );
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document.write( "N a Sum <BR>\n" );
document.write( "0 1 1 <BR>\n" );
document.write( "1 0.5 1.5 <BR>\n" );
document.write( "2 0.25 1.75 <BR>\n" );
document.write( "3 0.125 1.875 <BR>\n" );
document.write( "4 0.0625 1.9375 <BR>\n" );
document.write( "5 0.03125 1.96875 <BR>\n" );
document.write( "6 0.015625 1.984375 <BR>\n" );
document.write( "7 0.007813 1.992188 <BR>\n" );
document.write( "8 0.003906 1.996094 <BR>\n" );
document.write( "9 0.001953 1.998047 <BR>\n" );
document.write( "10 0.000977 1.999023 <BR>\n" );
document.write( "11 0.000488 1.999512 <BR>\n" );
document.write( "12 0.000244 1.999756 \r<BR>\n" );
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