document.write( "Question 867959: The sum of first 12 terms of an A.P. is 28 and the sum of its first 28 terms is 12 ; find the sum of its first 40 terms.ans is
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Algebra.Com's Answer #523291 by MathTherapy(10552)\"\" \"About 
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\n" ); document.write( "The sum of first 12 terms of an A.P. is 28 and the sum of its first 28 terms is 12 ; find the sum of its first 40 terms.ans is
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document.write( "With \"S%5B12%5D+=+28\", and n = 12, the sum of an A.P. formula: \"S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29\" becomes:
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document.write( "\"S%5B12%5D+=+%2812%2F2%29%282a%5B1%5D+%2B+%2812+-+1%29d%29\"  
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document.write( "\"28+=+6%282a%5B1%5D+%2B+11d%29\" 
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document.write( "\"2a%5B1%5D+%2B+11d+=+28%2F6\"  
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document.write( "\"2a%5B1%5D+%2B+11d+=+14%2F3\"
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document.write( "\"6a%5B1%5D+%2B+33d+=+14\" ---------- Multiplying by LCD, 3\r
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document.write( "With \"S%5B28%5D+=+12\", and n = 28, the sum of an A.P. formula: \"S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29\" becomes:
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document.write( "\"S%5B28%5D+=+%2828%2F2%29%282a%5B1%5D+%2B+%2828+-+1%29d%29\"  
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document.write( "\"12+=+14%282a%5B1%5D+%2B+27d%29\" 
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document.write( "\"2a%5B1%5D+%2B+27d+=+12%2F14\"  
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document.write( "\"2a%5B1%5D+%2B+27d+=+6%2F7\"
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document.write( "\"14a%5B1%5D+%2B+189d+=+6\" ---------- Multiplying by LCD, 7\r
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document.write( "\"6a%5B1%5D+%2B+33d+=+14\" --------- eq (i)
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document.write( "\"14a%5B1%5D+%2B+189d+=+6\" -------- eq (ii)
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document.write( "\"42a%5B1%5D+%2B+231d+=+98\" ------- Multiplying eq (i) by 7 ------ eq (iii)
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document.write( "\"-+42a%5B1%5D+-+567d+=+-+18\" ---- Multiplying eq (ii) by – 3 ----- eq (iv)
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document.write( "- 336d = 80 ---------- Adding eqs (iv) & (iii)
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document.write( "d, or common difference = \"80%2F-+336\", or \"-+5%2F21\"\r
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document.write( "\"6a%5B1%5D+%2B+33%28-+5%2F21%29+=+14\" ------- Substituting \"-+5%2F21\" for d in eq (i) 
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document.write( "\"6a%5B1%5D+%2B+11%28-+5%2F7%29+=+14\"
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document.write( "\"6a%5B1%5D+-+55%2F7+=+14\"
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document.write( "\"42a%5B1%5D+-+55+=+98\" ------ Multiplying by LCD, 7 
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document.write( "\"42a%5B1%5D+=+98+%2B+55\"
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document.write( "\"42a%5B1%5D+=+153\"
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document.write( "\"a%5B1%5D+=+153%2F42\", or \"51%2F14\"\r
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document.write( "\"S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29\"
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document.write( "\"S%5B40%5D+=+%2840%2F2%29%282%2851%2F14%29+%2B+%2840+-+1%29%28-+5%2F21%29%29\"
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document.write( "\"S%5B40%5D+=+20%2851%2F7+%2B+39%28-+5%2F21%29%29\"
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document.write( "\"S%5B40%5D+=+20%28153%2F21+-+195%2F21%29\"
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document.write( "\"S%5B40%5D+=+20%28-+42%2F21%29\"
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document.write( "Sum of the 1st 40 terms, or \"S%5B40%5D+=+20%28-+2%29\", or \"highlight_green%28S%5B40%5D+=+-+40%29\"
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document.write( "You can do the check!! \r
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document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
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document.write( "Further help is available, online or in-person, for a fee, obviously.  \n" );
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