document.write( "Question 1202468: Calculate the sum between and including the terms t16 and t53 of an arithmetic sequence with first term 543 and common difference - 12. \n" ); document.write( "

Algebra.Com's Answer #837335 by ikleyn(52792) $\"\"$ $\"About$

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\n" ); document.write( "Calculate the sum between and including the terms t16 and t53 of an arithmetic sequence
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\n" ); document.write( "\n" ); document.write( "            The solution by @mananth is a pile of mistakes,\r
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\n" ); document.write( "\n" ); document.write( "            I came to bring a correct solution.\r
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document.write( "There are two ways to solve the problem.\r\n" );
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document.write( "                          First way\r\n" );
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document.write( "The needed sum is the difference  S(t16,t53) = S(53) - S(15).      (1)\r\n" );
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document.write( "The sum of the first 53 terms is (use the standard formula for the sum\r\n" );
document.write( "of n first terms of an AP)\r\n" );
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document.write( "    S(53) =  =  = 12243.     (2)\r\n" );
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document.write( "The sum of the first 15 terms is (use the same standard formula for the sum\r\n" );
document.write( "of n first terms of an AP)\r\n" );
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document.write( "    S(15) =  =  = 6885.      (3)\r\n" );
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document.write( "Now the  ANSWER  is the difference of numbers (2) and (3), according to (1):\r\n" );
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document.write( "    S(t16,t53) = S(53) - S(15) = 12243 - 6885 = 5358.             (4)    ANSWER\r\n" );
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document.write( "                          Second way\r\n" );
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document.write( "Second way is to calculate the terms of this AP\r\n" );
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document.write( "    t16 = 543 + (16-1)*(-12) = 363,  t53 = 543 + (53-1)*(-12) = -81,\r\n" );
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document.write( "and then use another standard formula for the sum \r\n" );
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document.write( "    S(t16,t53) =  =  = 5358.    (5)\r\n" );
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document.write( "We get the same number/answer as in (4).\r\n" );
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document.write( "ANSWER.  The needed sum is 5358,  calculated in two different ways.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Regarding work of @mananth at this forum, I always repeat it many times,
\n" ); document.write( "that his work can be successful under two indispensable conditions:\r
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\n" ); document.write( "\n" ); document.write( " - two persons should assist him: one to explain him what to do,
\n" ); document.write( " and the second to re-write and edit his compositions after him.\r
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