document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=751047>Question 751047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A father opens a bank account when his daughter is born and deposits $5. Each year on her birthday he deposits twice the amount that he did in the previous year (i.e. on her first birthday he deposits $10). He continues this until she is 16 years old. Assuming that no interest is paid, how much is in the account after this time. This is a nonlinear equation but is also a nonlinear sequence can you help me find the Tn=?<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 #456987 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A father opens a bank account when his daughter is born and deposits $5. Each year on her birthday he deposits twice the amount that he did in the previous year (i.e. on her first birthday he deposits $10). He continues this until she is 16 years old.\r<BR>\n" );
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document.write( "5, 10, 20, 40, 80, 160, 320, 640, .... \r<BR>\n" );
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document.write( "(x(sub 1))=5 and any element in the sequence is 2(x(sub i -1))  where i = 2,3,...16\r<BR>\n" );
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document.write( "we want the summation of x(sub i)  where i = 1,2,3,...16\r<BR>\n" );
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document.write( "observe that this is a Geometric progression, that is, the quotient of any two successive members of the sequence is a constant\r<BR>\n" );
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document.write( "in our sequence we see 10/5 = 2, 20/10 = 2, 40/20=2\r<BR>\n" );
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document.write( "for our problem the common ratio (q) is 2 and the scale factor is 5\r<BR>\n" );
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document.write( "formula for the sum of the first n numbers of a geometric series is\r<BR>\n" );
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document.write( "s(sub n) = x(sub 1) * (1 - q^n) / (1-q)\r<BR>\n" );
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document.write( "s(sub 16) = 5 * (1 - 2^16) / (1-2)<BR>\n" );
document.write( "s(sub 16) = 5 * (1 - 65536) / (-1)<BR>\n" );
document.write( "s(sub 16) = 5 * 65535<BR>\n" );
document.write( "s(sub 16) = 327,675\r<BR>\n" );
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