document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144811>Question 1144811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me this question\r<BR>\n" );
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document.write( "If A,B,C and X,Y,Z are are two arithmetic sequence,then A+x,B+y,C+Z is are arithmetic sequence </SPAN>\n" );
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document.write( "A,B,C is arithmetic meaning that<BR>\n" );
document.write( "B = A+d<BR>\n" );
document.write( "C = B+d = (A+d)+d = A+2d\r<BR>\n" );
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document.write( "In other words: <BR>\n" );
document.write( "A,B,C<BR>\n" );
document.write( "turns into<BR>\n" );
document.write( "A,A+d,A+2d<BR>\n" );
document.write( "for some real number d. Each new term is found by adding some number onto the prior term.  \r<BR>\n" );
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document.write( "Through similar logic, we can turn<BR>\n" );
document.write( "X,Y,Z<BR>\n" );
document.write( "into<BR>\n" );
document.write( "X,X+e,X+2e<BR>\n" );
document.write( "where 'e' plays the same role as d above in the prior sequence.\r<BR>\n" );
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document.write( "Add the sequences by pairing up the corresponding values<BR>\n" );
document.write( "A+X = A+X<BR>\n" );
document.write( "B+Y = (A+d)+(X+e) = (A+X) + (d+e)<BR>\n" );
document.write( "C+Z = (A+2d)+(X+2e) = (A+X) + (2d+2e) = (A+X)+2(d+e)\r<BR>\n" );
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document.write( "As you can see, the sequence<BR>\n" );
document.write( "A+X, (A+X) + (d+e), (A+X)+2(d+e)<BR>\n" );
document.write( "is in the form A+n*d which is of arithmetic form\r<BR>\n" );
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document.write( "Therefore, the original claim is true.<BR>\n" );
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