document.write( "Question 1078619: If (a_1,a_2,..a_17) satisfy\r
\n" ); document.write( "\n" ); document.write( "a_1 + a_2 + a_3 = 1,
\n" ); document.write( "a_2 + a_3 + a_4 = 2,
\n" ); document.write( "a_3 + a_4 + a_5 = 3, \r
\n" ); document.write( "\n" ); document.write( "a_{15} + a_{16} + a_{17} = 15,
\n" ); document.write( "a_{16} + a_{17} + a_{1} = 16,
\n" ); document.write( "a_{17} + a_{1} + a_{2} = 17,
\n" ); document.write( "
\n" ); document.write( "what is the value of a_{17}?
\n" ); document.write( "what is the value of $a_{17}$? \n" ); document.write( "

Algebra.Com's Answer #693189 by ikleyn(52909) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "I read your problem in THIS way:

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document.write( "If (,, . . . ) satisfy\r\n" );
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document.write( " = 1, \r\n" );
document.write( " = 2,\r\n" );
document.write( " = 3, \r\n" );
document.write( ". . . . . . . . .        <<<---=== I added THIS which means that there are similar equations for all intermediate indexes\r\n" );
document.write( " = 15, \r\n" );
document.write( " = 16, \r\n" );
document.write( " = 17\r\n" );
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document.write( "what is the value of  ?

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document.write( "Below is the system of equations written in full\r\n" );
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document.write( " = 1,        (1)\r\n" );
document.write( " = 2,        (2)\r\n" );
document.write( " = 3,        (3) \r\n" );
document.write( " = 4,        (4) \r\n" );
document.write( " = 5,        (5)\r\n" );
document.write( " = 6,        (6)\r\n" );
document.write( " = 7,        (7) \r\n" );
document.write( " = 8,       (8) \r\n" );
document.write( " = 9,      (9)\r\n" );
document.write( " = 10,    (10) \r\n" );
document.write( " = 11,    (11) \r\n" );
document.write( " = 12,    (12) \r\n" );
document.write( " = 13,    (13)\r\n" );
document.write( " = 14,    (14)\r\n" );
document.write( " = 15,    (15)\r\n" );
document.write( " = 16,     (16)\r\n" );
document.write( " = 17.      (17)\r\n" );
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document.write( "Add all 17 equations (1) - (17)  (both sides). You will get\r\n" );
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document.write( " = 1 + 2 + 3 + . . . + 15 + 16 + 17 =  = 9*17 = 153.\r\n" );
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document.write( "Now divide both sides of the lest equation by 3, and you will get\r\n" );
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document.write( " = 51.   (18)\r\n" );
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document.write( "Next subtract equation (1) from the equation (18). You will get\r\n" );
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document.write( " = 51 - 1 = 50.   (19)\r\n" );
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document.write( "Next subtract equation (4) from the equation (19). You will get\r\n" );
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document.write( " = 50 - 4 = 46.   (20)\r\n" );
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document.write( "Next subtract equation (7) from the equation (20). You will get\r\n" );
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document.write( " = 46 - 7 = 39.   (21)\r\n" );
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document.write( "Next subtract equation (10) from the equation (21). You will get\r\n" );
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document.write( " = 39 - 10 = 29.   (22)\r\n" );
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document.write( "Next subtract equation (13) from the equation (22). You will get\r\n" );
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document.write( " = 29 - 13 = 16.   (23)\r\n" );
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document.write( "Now compare equations (23) and (16). You instantly will get \r\n" );
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document.write( " = 16 - 16 = 0.                  (24)\r\n" );
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document.write( "Having known  = 0, we can rewrite the equation (18) in the form\r\n" );
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document.write( " = 51.   (25)\r\n" );
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\n" ); document.write( "\n" ); document.write( " Now we are on the finish line, finally !!!\r
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document.write( "Next subtract equation (2) from the equation (25). You will get\r\n" );
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document.write( " = 51 - 2 = 49.   (26)\r\n" );
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document.write( "Next subtract equation (5) from the equation (25). You will get\r\n" );
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document.write( " = 49 - 5 = 44.   (27)\r\n" );
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document.write( "Next subtract equation (8) from the equation (27). You will get\r\n" );
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document.write( " = 44 - 8 = 36.   (28)\r\n" );
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document.write( "Next subtract equation (11) from the equation (28). You will get\r\n" );
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document.write( " = 36 - 11 = 25.   (29)\r\n" );
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document.write( "As the last step, subtract equation (14) from the equation (29). You will get\r\n" );
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document.write( " = 25 - 14 = 11.   (30)\r\n" );
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document.write( "It is your answer:   = 11.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. $\"a%5B17%5D\"$ = 11.\r
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