document.write( "Question 35713This question is from textbook Algebra and Trigonometry
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Algebra.Com's Answer #21875 by AnlytcPhil(1810)\"\" \"About 
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40,-20,10,-5,...:t8\r\n" );
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document.write( "Four terms are listed.  Ask yourself the following questions \r\n" );
document.write( "about them:\r\n" );
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document.write( "What do you have to do to the 1st term to get the 2nd, that is,\r\n" );
document.write( "What do you have to do to 40 to get -20?\r\n" );
document.write( "Two possible answers are  (1) add -60; (2) multiply by -1/2\r\n" );
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document.write( "What do you have to do to the 2nd term to get the 3rd, that is,\r\n" );
document.write( "What do you have to do to -20 to get 10?\r\n" );
document.write( "Two possible answers are  (1) add 30; (2) multiply by -1/2\r\n" );
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document.write( "What do you have to do to the 3rd term to get the 4th, that is,\r\n" );
document.write( "What do you have to do to 10 to get -5?\r\n" );
document.write( "Two possible answers are  (1) add -15; (2) multiply by -1/2\r\n" );
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document.write( "The only answer common to all these is (2) multiply by -1/2\r\n" );
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document.write( "So it is an geometric sequence with t1 = 40, and r = -1/2\r\n" );
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document.write( "tn = t1(1-rn)/(1-r) \r\n" );
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document.write( "we are looking for t8, so n=8, t1 = 40, r = -1/2\r\n" );
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document.write( "t8 = 40[1-(-1/2)8]/[1-(-1/2)]\r\n" );
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document.write( "t8 = 40(1-1/256)/(1+1/2)\r\n" );
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document.write( "t8 = 40(255/256)/(3/2)\r\n" );
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document.write( "t8 = 40(255/256)×(2/3) \r\n" );
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document.write( "t8 = 425/16 or 26.5625\r\n" );
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document.write( "Checking with a calculator:\r\n" );
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document.write( "t1 = 40\r\n" );
document.write( "t2 = -20\r\n" );
document.write( "t3 = 10\r\n" );
document.write( "t4 = -5\r\n" );
document.write( "t5 = 2.5\r\n" );
document.write( "t6 = -1.25\r\n" );
document.write( "t7 = .625\r\n" );
document.write( "t8 = -.3125\r\n" );
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document.write( "Adding them all up, 40-20+10-5+2.5-1.25+.625-.3125 = 26.5625\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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