document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202469>Question 1202469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The 3rd term of a geometric sequence is 36, and the 6th term is 9/2. What is the recursive formula for the sequence? </SPAN>\n" );
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document.write( "The 3rd term, 36, is the first term, multiplied by the common ratio 2 times: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2=36 ALIGN=MIDDLE  ALT=\"ar%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The 6th term, 9/2, is the first term, multiplied by the common ratio 5 times: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E5=9%2F2 ALIGN=MIDDLE  ALT=\"ar%5E5=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Divide the formulas for the 6th and 3rd terms to calculate the common ratio:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=%289%2F2%29%2F36=1%2F8 ALIGN=MIDDLE  ALT=\"r%5E3=%289%2F2%29%2F36=1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1%2F2 ALIGN=MIDDLE  ALT=\"r=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A RECURSIVE formula tells how to get each term from the preceding term; for a geometric sequence the rule is \"multiply by the common ratio\".  Since in this problem the common ratio is 1/2, the recursive formula is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28n%29=%281%2F2%29%2Aa%28n-1%29 ALIGN=MIDDLE  ALT=\"a%28n%29=%281%2F2%29%2Aa%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To complete the definition of the recursive formula for the sequence, we need to specify the first term.  Since the 3rd term is 36 and the common ratio is 1/2,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=a%28%281%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"36=a%28%281%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=a%2F4 ALIGN=MIDDLE  ALT=\"36=a%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=144 ALIGN=MIDDLE  ALT=\"a=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: a(1)=144; for n>1, a(n)=(1/2)*a(n-1)<br><BR>\n" );
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