document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446254>Question 446254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> true or false. the sequence a(n)=2,4,8,16,32,...is the same as the sequence a(1)=2, a(n)=2a(n-1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307310 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</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=307310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <pre<<BR>\n" );
document.write( "What we need to find out is whether the five things<BR>\n" );
document.write( "that are true for \r<BR>\n" );
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document.write( "a(n)=2,4,8,16,32,... \r<BR>\n" );
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document.write( "are also true for  \r<BR>\n" );
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document.write( "a(1)=2, a(n)=2a(n-1)\r<BR>\n" );
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document.write( "If so the answer is \"yes\"; otherwise \"no\". <BR>\n" );
document.write( "Below are the five things that are true for<BR>\n" );
document.write( "the first that must also be true for the<BR>\n" );
document.write( "second in order for the correct answer to <BR>\n" );
document.write( "be \"true\":\r<BR>\n" );
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document.write( "A.  a(1) = 2<BR>\n" );
document.write( "B.  a(2) = 4<BR>\n" );
document.write( "C.  a(3) = 8<BR>\n" );
document.write( "D.  a(4) = 16<BR>\n" );
document.write( "E.  a(5) = 32\r<BR>\n" );
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document.write( "We are told that <BR>\n" );
document.write( "a(1) = 2\r<BR>\n" );
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document.write( "So we know that A. is true\r<BR>\n" );
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document.write( "Now we will substitute n = 2 to see if B. is true.\r<BR>\n" );
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document.write( "a(n)=2a(n-1)<BR>\n" );
document.write( "a(2)=2a(2-1)=2a(1)=2*2 = 4\r<BR>\n" );
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document.write( "So now we know that B. is true\r<BR>\n" );
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document.write( "Now we will substitute n = 3 to see if C. is true.\r<BR>\n" );
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document.write( "a(n)=2a(n-1)<BR>\n" );
document.write( "a(3)=2a(3-1)=2a(2)=2*4 = 8\r<BR>\n" );
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document.write( "So now we know that C. is true\r<BR>\n" );
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document.write( "Now we will substitute n = 4 to see if D. is true.\r<BR>\n" );
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document.write( "a(n)=2a(n-1)<BR>\n" );
document.write( "a(4)=2a(4-1)=2a(3)=2*8 = 16\r<BR>\n" );
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document.write( "So now we know that D. is true\r<BR>\n" );
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document.write( "Now we will substitute n = 5 to see if E. is true.\r<BR>\n" );
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document.write( "a(n)=2a(n-1)<BR>\n" );
document.write( "a(5)=2a(5-1)=2a(4)=2*16 = 32\r<BR>\n" );
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document.write( "So now we know that E. is true\r<BR>\n" );
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document.write( "Since they are all true, the answer is \"yes\".\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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