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 #837417 by MathTherapy(10552)\"\" \"About 
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document.write( "Calculate the sum between and including the terms t16 and t53 of an arithmetic sequence with first term 543 and common difference  -  12.\r\n" );
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document.write( "use the A.P. formula to get the value of term 16 (t16 or a16).\r\n" );
document.write( "So, we get: \"matrix%281%2C3%2C+a%5Bn%5D%2C+%22=%22%2C+a%5B1%5D+%2B+%28n+-+1%29d%29\" ---- Formula for a specific term of an A.P./A.S.\r\n" );
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document.write( "Now, we use the formula for the sum of an A.P. series from term 16 to term 53. The number of terms (n) in this series = 38 (53 - 16 + 1)\r\n" );
document.write( "Additionally, note that since we're summing the values from the 16th term to the 53rd term, we will use term 16 as the 1st term of the series.\r\n" );
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document.write( "So, we get: \"matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29\" ---- Formula for the sum of an A.P./A.S.\r\n" );
document.write( "            ---- Substituting 38 for n, 363 for a1, and - 12 for d\r\n" );
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document.write( "From term 16 (t16, or a16) to term 53 (t53, or a53), SUM of the series, or S38 = 19(282) = 5,358\r\n" );
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document.write( "OR\r\n" );
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document.write( "Find the sum of ALL 53 terms:\r\n" );
document.write( "            \"matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29\" ---- Formula for the sum of an A.P./A.S.\r\n" );
document.write( "            ---- Substituting 53 for n, 543 for a1, and - 12 for d\r\n" );
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document.write( "SUM of ALL 53 terms = 53(231) = 12,243\r\n" );
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document.write( "Find the sum of the FIRST 15 terms:\r\n" );
document.write( "            \"matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29\" ---- Formula for the sum of an A.P./A.S.\r\n" );
document.write( "            ---- Substituting 15 for n, 543 for a1, and - 12 for d\r\n" );
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document.write( "SUM of FIRST 15 terms = 15(459) = 6,885\r\n" );
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document.write( "Now, SUBTRACT the SUM of the 1st 15 terms from the SUM of ALL 53 terms to get the SUM of terms 16 to 53.\r\n" );
document.write( "This is: 12,243 - 6,885 = 5,358
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