document.write( "Question 1134278: The sixth & eleventh terms of a linear sequence are respectively 23 & 48. Calculate the sum of the first twenty terms \n" ); document.write( "

Algebra.Com's Answer #751614 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "There are  11-6 = 5 gaps between the 6-th and 11-th terms; so each gap (which is the common difference of the AP) is\r\n" );
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document.write( "     =  = 5.\r\n" );
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document.write( "Hence, the first term is\r\n" );
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document.write( "     =  = 23 - 5*5 = 23 - 25 = -2,\r\n" );
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document.write( "while the 20-th term is \r\n" );
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document.write( "     =  = -2 + 19*5 = 93.\r\n" );
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document.write( "The sum    of the first 20 terms is 20 times the average of the 1-th and 20-th terms\r\n" );
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document.write( "     =  =  = (-2+93)*10 = 91*10 = 910.     ANSWER\r\n" );
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document.write( "CHECK   (Thanks to my MS Excel )\r\n" );
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document.write( "n      \r\n" );
document.write( "------------------\r\n" );
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document.write( "1	-2\r\n" );
document.write( "2	3\r\n" );
document.write( "3	8\r\n" );
document.write( "4	13\r\n" );
document.write( "5	18\r\n" );
document.write( "6	23\r\n" );
document.write( "7	28\r\n" );
document.write( "8	33\r\n" );
document.write( "9	38\r\n" );
document.write( "10	43\r\n" );
document.write( "11	48\r\n" );
document.write( "12	53\r\n" );
document.write( "13	58\r\n" );
document.write( "14	63\r\n" );
document.write( "15	68\r\n" );
document.write( "16	73\r\n" );
document.write( "17	78\r\n" );
document.write( "18	83\r\n" );
document.write( "19	88\r\n" );
document.write( "20	93\r\n" );
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document.write( "Sum = 	910\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( "    - 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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