document.write( "Question 1208674: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms \n" ); document.write( "

Algebra.Com's Answer #847069 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "The 10th and 15th terms of an AP are -5 and -15/2 respectively. what is the sum of the first 20 terms
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document.write( "The 10th term is -5;  the 15th term is -15/2 = -7.5.\r\n" );
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document.write( "The difference between the 15th term and the 10th term is -7.5 - (-5) = -7.5 + 5 = -2.5.\r\n" );
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document.write( "Between the 10th term and 15th term, there are 5 equal gaps, each equal to the common difference d.\r\n" );
document.write( "so, the common difference d = -2.5/5 = -0.5.\r\n" );
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document.write( "The 10th term is -5,  so   + 9d = -5,   = -5 -9*(-0.5) = -5 + 4.5 = -0.5.\r\n" );
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document.write( "The 20th term is   =  + 19*(-0.5) = -0.5 - 9.5 = -10.\r\n" );
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document.write( "Thus the sum of the first 20 terms of the AP is\r\n" );
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document.write( "     =  =  =  = -10.5*10 = -105.\r\n" );
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document.write( "ANSWER.  The sum of the first 20 terms of the AP is -105.\r\n" );
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