document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083614>Question 1083614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the common difference, d of the sequence shown below?\r<BR>\n" );
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document.write( "-1, -5, -9, -13, -17, -21, …\r<BR>\n" );
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document.write( "A) 4<BR>\n" );
document.write( "B) -4<BR>\n" );
document.write( "C) -1<BR>\n" );
document.write( "D) -5 </SPAN>\n" );
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document.write( "Answer: <font color=red>Choice B) -4</font><BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Pick any term but the first one. Whatever term you picked, subtract off the previous term\r<BR>\n" );
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document.write( "Let's say you picked the third term -9. The previous term is -5. Subtract these values:\r<BR>\n" );
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document.write( "(term picked) - (previous term) = (-9) - (-5)<BR>\n" );
document.write( "(term picked) - (previous term) = -9 + 5<BR>\n" );
document.write( "(term picked) - (previous term) = -4\r<BR>\n" );
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document.write( "which is the common difference. \r<BR>\n" );
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document.write( "Let's try another selection. Pick the fifth term -17<BR>\n" );
document.write( "The previous term is -13\r<BR>\n" );
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document.write( "(term picked) - (previous term) = (-17) - (-13)<BR>\n" );
document.write( "(term picked) - (previous term) = -17 + 13<BR>\n" );
document.write( "(term picked) - (previous term) = -4\r<BR>\n" );
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document.write( "we get the same result. This will happen with any selection you make. You can't pick on the first term because there's no known terms before it. \r<BR>\n" );
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document.write( "Note how each term is decreasing by 4 each time. This is another way to see that the common difference is -4\r<BR>\n" );
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document.write( "As you can see<BR>\n" );
document.write( "second term = (first term) + (common difference) = -1 + (-4) = -5<BR>\n" );
document.write( "third term = (second term) + (common difference) = -5 + (-4) = -9<BR>\n" );
document.write( "fourth term = (third term) + (common difference) = -9 + (-4) = -13<BR>\n" );
document.write( "fifth term = (fourth term) + (common difference) = -13 + (-4) = -17<BR>\n" );
document.write( "and so on...\r<BR>\n" );
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