document.write( "Question 310023: can you help. I am trying to help my son with his algebra homework. His school does not send books home and I haven't used some of this in 20 years. The problem states.\r
\n" ); document.write( "\n" ); document.write( "Write an equation for the nth term of -23,38,99,160\r
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\n" ); document.write( "a. $\"a%5Bn%5D=38n-61\"$
\n" ); document.write( "b. $\"a%5Bn%5D=61n-24\"$
\n" ); document.write( "c. $\"a%5Bn%5D=61n-84\"$
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Algebra.Com's Answer #221762 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I think you need a more detailed explanation than the other tutor gave,\r\n" );
document.write( "although his is correct.\r\n" );
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document.write( "First note that those n's are SUBscripts, not exponents (which are SUPERscripts).\r\n" );
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document.write( "The numbers -23,38,99,160 means:\r\n" );
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document.write( "FIRST TERM = \r\n" );
document.write( "SECOND TERM = \r\n" );
document.write( "THIRD TERM = \r\n" );
document.write( "FOURTH TERM = \r\n" );
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document.write( "In math there are two ways to handle a multiple choice question.\r\n" );
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document.write( "Method 1.  Do the problem as you were taught and mark the choice\r\n" );
document.write( "           that corresponds to your answer. \r\n" );
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document.write( "Method 2.  Go through the choices and find the one that satisfies\r\n" );
document.write( "           all the conditions given in the problem.\r\n" );
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document.write( "The instructor, of course, hopes that the student will use Method 1. \r\n" );
document.write( "if the test is objective, then the student must do the problem as\r\n" );
document.write( "taught.  However in multiple choice exams, when the student is not \r\n" );
document.write( "sure how to do the problem, Method 2 will often, but not always, \r\n" );
document.write( "lead to the correct answer. This is a case where Method 2 will work!\r\n" );
document.write( "So I will begin with Method 2, then I will use Method 1.\r\n" );
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document.write( "First try choice a.  to see if  by \r\n" );
document.write( "substituting :\r\n" );
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document.write( "         \r\n" );
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document.write( "That works, but now we must make sure it works when n=2, 3, and 4.\r\n" );
document.write( "So we see if  by substituting \r\n" );
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document.write( "So we see that gives 15, not 38, so we can rule out choice a.\r\n" );
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document.write( "Next try choice b.  to see if  by \r\n" );
document.write( "substituting  to see if :\r\n" );
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document.write( "         \r\n" );
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document.write( "So we see that gives 15, not 38, so we can rule out choice b\r\n" );
document.write( "just by checking only \r\n" );
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document.write( "Next try choice c.  to see if  by \r\n" );
document.write( "substituting :\r\n" );
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document.write( "         \r\n" );
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document.write( "That works, but now we must make sure it works when n=2, 3, and 4.\r\n" );
document.write( "So we see if  by substituting \r\n" );
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document.write( "         \r\n" );
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document.write( "That works, too, but now we must make sure it works when n=3 and 4.\r\n" );
document.write( "So we see if  by substituting \r\n" );
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document.write( "That works, too, but now we only need to make sure it works when n=4.\r\n" );
document.write( "So we see if  by substituting \r\n" );
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document.write( "So now we know for sure that c is the correct choice.  We don't need to\r\n" );
document.write( "try d, but if we do, we'll find that it gives \r\n" );
document.write( "and so is quickly eliminated. \r\n" );
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document.write( "Next we'll do it by Method 1, the way your son was taught, although \r\n" );
document.write( "you should tell him to use Method 2 on multiple choice exams when he \r\n" );
document.write( "is not sure how to start.\r\n" );
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document.write( "Method 1.\r\n" );
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document.write( "First we determine whether this is a geometric or an arithmetic sequence.\r\n" );
document.write( "[20 years ago these were called \"progressions\", but in modern times, they\r\n" );
document.write( "are called \"sequences\".]\r\n" );
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document.write( "If it is a geometric sequence, then \r\n" );
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document.write( ", the common ratio.\r\n" );
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document.write( "If it is arithmetic, then \r\n" );
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document.write( ", the common difference.\r\n" );
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document.write( "For it to be geometric,\r\n" );
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document.write( "This is certainly FALSE, so we know that it is not geometric.\r\n" );
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document.write( "For it to be arithmetic,\r\n" );
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document.write( "This is certainly TRUE, so we know that it is an arithmetic sequence.\r\n" );
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document.write( "Your son was taught formulas for the nth terms of both types of \r\n" );
document.write( "sequences.  He was taught that the formula for the nth term of\r\n" );
document.write( "an arithmetic sequence is\r\n" );
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document.write( "So we substitute  and \r\n" );
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document.write( "And using Method 1 we see that the correct choice is c.\r\n" );
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document.write( "[In case he has other sequence problems that are geometric,\r\n" );
document.write( "the formula for the nth term is ].\r\n" );
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document.write( "Edwin

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