document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151136>Question 1151136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three numbers are in an arithmetic progression with a common difference of 6. If 4 is subtracted from the first number, 1 is subtracted from the second number, and the third number is first decreased by 3 and then multiplied by 3, then the resulting three numbers form a geometric progression. Find the original three numbers. </SPAN>\n" );
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document.write( "Let the original three numbers be x-6, x, and x+6.<br><BR>\n" );
document.write( "Then (x-6)-4 = x-10, x-1, and 3((x+6)-3) = 3x+9 form a geometric progression, which means there is a common ratio between the terms.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x-10%29+=+%283x%2B9%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x-10%29+=+%283x%2B9%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-21x-90+=+x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"3x%5E2-21x-90+=+x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-19x-91+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2-19x-91+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B7%29%28x-13%29+=+0 ALIGN=MIDDLE  ALT=\"%282x%2B7%29%28x-13%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7%2F2 ALIGN=MIDDLE  ALT=\"x+=+-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Both solutions satisfy the conditions of the problem.<br><BR>\n" );
document.write( "(A) x = -7/2:<br><BR>\n" );
document.write( "The original arithmetic progression is<br><BR>\n" );
document.write( "-19/2, -7/2, 5/2<br><BR>\n" );
document.write( "When 4 is subtracted from the first term, 1 is subtracted from the second term, and the third term is decreased by 3 and then multiplied by 3, the resulting numbers form a geometric progression:<br><BR>\n" );
document.write( "-27/2, -9/2, -3/2<br><BR>\n" );
document.write( "(B) x = 13:<br><BR>\n" );
document.write( "The original arithmetic progression is<br><BR>\n" );
document.write( "7, 13, 19<br><BR>\n" );
document.write( "When 4 is subtracted from the first term, 1 is subtracted from the second term, and the third term is decreased by 3 and then multiplied by 3, the resulting numbers form a geometric progression:<br><BR>\n" );
document.write( "3, 12, 48<br><BR>\n" );
document.write( " </SPAN>\n" );
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