document.write( "Question 1163799: Question: \"The sum of 40 terms of a certain arithmetic sequence is 430, while the sum of 60 terms is 945. Determine the nth term of the arithmetic sequence.\"\r
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Algebra.Com's Answer #788005 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "The sum of 40 terms of a certain arithmetic sequence is 430, while the sum of 60 terms is 945.
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document.write( "The sum of any AP is the average of its extreme terms times the number of terms.\r\n" );
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document.write( "So, from the condition\r\n" );
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document.write( "    \"%28%28a%5B1%5D%2Ba%5B40%5D%29%2F2%29%2A40\" = 430.\r\n" );
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document.write( "    \"%28%28a%5B1%5D%2Ba%5B60%5D%29%2F2%29%2A60\" = 945.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "    \"a%5B1%5D+%2B+a%5B40%5D\" = \"%28430%2A2%29%2F40\" = 21.5     (1)\r\n" );
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document.write( "    \"a%5B1%5D+%2B+a%5B60%5D\" = \"%28945%2A2%29%2F60\" = 31.5     (2)\r\n" );
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document.write( "Now subtract equation (1) from equation (2)\r\n" );
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document.write( "    \"a%5B60%5D\" - \"a%5B40%5D\" = 31.5 - 21.5 = 10.\r\n" );
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document.write( "But   \"a%5B60%5D\" - \"a%5B40%5D\" = 20d,  where \"d\"  is the common difference.\r\n" );
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document.write( "Hence,  d = 10/20 = 0.5.\r\n" );
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document.write( "Next,  from equation (1)\r\n" );
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document.write( "    \"a%5B1%5D\" + \"a%5B1%5D%2B39%2A0.5\" = 21.5;\r\n" );
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document.write( "hence,\r\n" );
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document.write( "    \"a%5B1%5D\" = \"%2821.5+-+39%2A0.5%29%2F2\" = 1.\r\n" );
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document.write( "Now the n-th term is   \"a%5Bn%5D\" = \"a%5B1%5D\" + (n-1)*d = 1 + (n-1)*0.5.        ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "My lessons on arithmetic progressions in this site are\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Chocolate bars and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Calculating partial sums of arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Finding number of terms of an arithmetic progression \r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Interior angles of a polygon and Arithmetic progression \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions solved MENTALLY \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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