document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84905>Question 84905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone help me with this?  I'm stuck again and don't understand this geometric sequence stuff.  Any help would be appreciated! \r<BR>\n" );
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document.write( "Use the geometric sequence of numbers 1, 3, 9, 27, 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" );
document.write( "Show work here\r<BR>\n" );
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document.write( "b) 	Using the formula for the nth term of a geometric sequence, what is the 10th term?<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work here.  \r<BR>\n" );
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document.write( "c) 	Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms? <BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Show work here  \r<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 #61180 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 4><b>\r\n" );
document.write( "Can anyone help me with this? I'm stuck again and don't \r\n" );
document.write( "understand this geometric sequence stuff. Any help would \r\n" );
document.write( "be appreciated!  Use the geometric sequence of numbers\r\n" );
document.write( "1, 3, 9, 27, to find the following:\r\n" );
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document.write( "a). What is r, the ratio between 2 consecutive terms? \r\n" );
document.write( "Answer: \r\n" );
document.write( "Show work here: \r\n" );
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document.write( "2nd term divided by 1st term = 3 ÷ 1 = 3\r\n" );
document.write( "3rd term divided by 2nd term = 9 ÷ 3 = 3\r\n" );
document.write( "4th term divided by 3rd term = 27 ÷ 9 = 3\r\n" );
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document.write( "Notice they all turned out to be 3.\r\n" );
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document.write( "That means that the common ratio, r, between terms, is 3.\r\n" );
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document.write( "That means that the rule for getting the next term\r\n" );
document.write( "is to multiply by 3.  \r\n" );
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document.write( "1 times 3 is 3.\r\n" );
document.write( "3 times 3 is 9.\r\n" );
document.write( "9 times 3 is 27.\r\n" );
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document.write( "The next term not written is 81. That's because\r\n" );
document.write( "27 times 3 is 81.\r\n" );
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document.write( "The next term after 81 that is not written is 243.\r\n" );
document.write( "That's because \r\n" );
document.write( "81 times 3 is 243 \r\n" );
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document.write( "And so on and on.\r\n" );
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document.write( "b) Using the formula for the nth term of a geometric \r\n" );
document.write( "sequence, what is the 10th term?\r\n" );
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document.write( "Answer: \r\n" );
document.write( "Show work here. \r\n" );
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document.write( "The formula for the nth term of a geometric series is\r\n" );
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document.write( "a<sub>n</sub> = a<sub>1</sub>r<sup>n-1</sup> [<i>Some books use t for a;\r\n" );
document.write( "if yours uses t then replace all the a's by t's</i>]\r\n" );
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document.write( "a<sub>10</sub> = a<sub>1</sub>r<sup>10-1</sup>\r\n" );
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document.write( "a<sub>10</sub> = a<sub>1</sub>r<sup>9</sup>\r\n" );
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document.write( "a<sub>1</sub> stands for the first term, which is 1, and r stands for \r\n" );
document.write( "the ratio between terms, which we found to be 3.\r\n" );
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document.write( "a<sub>10</sub> = 1(3)<sup>9</sup>\r\n" );
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document.write( "a<sub>10</sub> = 19683\r\n" );
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document.write( "Checking\r\n" );
document.write( "the 5th term is the 4th term times 3 which is 27 times 3 which is 81\r\n" );
document.write( "the 6th term is the 5th term times 3 which is 81 times 3 which is 143\r\n" );
document.write( "the 7th term is the 6th term times 3 which is 243 times 3 which is 729\r\n" );
document.write( "the 8th term is the 7th term times 3 which is 729 times 3 which is 2187\r\n" );
document.write( "the 9th term is the 8th term times 3 which is 2187 times 3 which is 6561\r\n" );
document.write( "the 10th term is the 8rd term times 3 which is 6561 times 3 which is 19683\r\n" );
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document.write( "c) Using the formula for the sum of a geometric sequence, \r\n" );
document.write( "what is the sum of the first 10 terms? \r\n" );
document.write( "Answer: \r\n" );
document.write( "Show work here \r\n" );
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document.write( "      a<sub>1</sub>(r<sup>n</sup> - 1)\r\n" );
document.write( "S<sub>n</sub> = ————————————\r\n" );
document.write( "        r - 1\r\n" );
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document.write( "        1(3<sup>10</sup> - 1)\r\n" );
document.write( "S<sub>10</sub> = ——————————————\r\n" );
document.write( "           3 - 1 \r\n" );
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document.write( "        1(59049 - 1)\r\n" );
document.write( "S<sub>10</sub> = ——————————————\r\n" );
document.write( "            2\r\n" );
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document.write( "       1(59048)\r\n" );
document.write( "S<sub>10</sub> = ——————————\r\n" );
document.write( "           2\r\n" );
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document.write( "        59048\r\n" );
document.write( "S<sub>10</sub> = ————————\r\n" );
document.write( "          2\r\n" );
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document.write( "S<sub>10</sub> = 29524  \r\n" );
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document.write( "Checking: To check add up all the\r\n" );
document.write( "terms found when we checked the (b) part.\r\n" );
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document.write( "               1\r\n" );
document.write( "               3\r\n" );
document.write( "               9\r\n" );
document.write( "              27\r\n" );
document.write( "              81\r\n" );
document.write( "             243\r\n" );
document.write( "             729\r\n" );
document.write( "            2187\r\n" );
document.write( "            6561\r\n" );
document.write( "        +  19683\r\n" );
document.write( "        --------\r\n" );
document.write( "Total =    29524\r\n" );
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document.write( "Edwin</PRE>  </SPAN>\n" );
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