document.write( "Question 1135971: The sum of the 1st and 2nd term of an A.P is 4 and the 10th term is 19.find the sum of the 5th and 6th term \n" ); document.write( "
Algebra.Com's Answer #753699 by ikleyn(52799)\"\" \"About 
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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "    \"a%5B1%5D\" + \"a%5B2%5D\" = 4\r\n" );
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document.write( "    \"a%5B1%5D\" + 9*d = 19.\r\n" );
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document.write( "Or, in the equivalent form,\r\n" );
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document.write( "    2a + d  = 4,     (1)\r\n" );
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document.write( "    a  + 9d = 19.    (2)\r\n" );
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document.write( "From eq(1), express  d = 4 - 2a and substitute it into eq(2). You will get\r\n" );
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document.write( "    a + 9*(4-2a) = 19,\r\n" );
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document.write( "    a + 36 - 18a = 19,\r\n" );
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document.write( "    -17a = 19 - 36 = -17  ===========>  a = \"%28-17%29%2F%28-17%29\" = 1.\r\n" );
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document.write( "Then from eq(1),  d = 4 - 2*1 = 2.\r\n" );
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document.write( "So, the arithmetic progression has the first term 1 and the common difference 2.\r\n" );
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document.write( "The progression is  1, 3, 5, 7, 9, 11, 13 . . . \r\n" );
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document.write( "The 5-th term is  1 + 4*2 = 9  and  the 6-th term is  1 + 5*2 = 11;\r\n" );
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document.write( "their sum is  9 + 11 = 20.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On this problem (in its earlier version), I wrote my post under the link\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1135935.html\r
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\n" ); document.write( "\n" ); document.write( "but obtained an \"UNSATISFIED\" response from the visitor - absolutely UNJUSTLY   (instead of his  (or her)  deepest \"THANKS\").\r
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\n" ); document.write( "\n" ); document.write( "            (After my explanation to the visitor that he (or she) absolutely incorrectly formulated the problem, \r
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\n" ); document.write( "\n" ); document.write( "            and after my explanation on how it should be done correctly - and after my solution.\r
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\n" ); document.write( "\n" ); document.write( "            I did not forget it . . . )\r
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