document.write( "Question 1144719: For a given arithmetic sequence, the 42nth term, a42, is equal to 194, and the 88th term, a88, is equal to 424.
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Algebra.Com's Answer #765888 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " = a + 41*d = 194.    (1)\r\n" );
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document.write( " = a + 87*d = 424.    (2)\r\n" );
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document.write( "The unknown \"a\" is the first term, and the unknown \"d\" is the common difference of the AP.\r\n" );
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document.write( "Thus you have the system of 2 linear equations in 2 unknown, so it is solvable.\r\n" );
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document.write( "The easiest way to solve it is to subtract equation (1) from equation (2). You will get\r\n" );
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document.write( "    87d - 41d = 424 - 194  \r\n" );
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document.write( "    46d       = 230\r\n" );
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document.write( "      d       = 230/46 = 5.\r\n" );
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document.write( "Then from equation (1),  a = 194 - 5*41 = -11.\r\n" );
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document.write( "Now you know EVERYTHING about your AP.  In particular,\r\n" );
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document.write( "     = a + 5*9 = -11 + 45 = 34.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\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( "    - 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( "    - Mathematical induction and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction for sequences other than arithmetic or geometric\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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\n" ); document.write( "\n" ); document.write( "                Come again soon to this forum to learn something new (!)\r
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