Algebra.Com's Answer #846151 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find the  value of k and the  17-th term of each of the following arithmetic sequence
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document.write( "6) 2k+1,5k-3, 7k-2
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document.write( "7) 7k+2,5k+4,4k-5
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document.write( " I will solve first part, leaving the second part to you as an exercise, \r
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document.write( " because the second part is a TWIN to the first part.\r
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document.write( "Since three terms  ,  and  form an arithmetic progression,\r\n" );
document.write( "the difference  is the same as the difference  \r\n" );
document.write( "(as each this difference is simply d, the common difference of the AP).\r\n" );
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document.write( "So, we write\r\n" );
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document.write( " (5k-3) - (2k+1) = (7k-2) - (5k-3).\r\n" );
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document.write( "From this equation, we find the value of k\r\n" );
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document.write( " 5k - 3 - 2k - 1 = 7k - 2 - 5k + 3,\r\n" );
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document.write( " 3k - 4 = 2k +1\r\n" );
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document.write( " 3k - 2k = 1 + 4\r\n" );
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document.write( " k = 5.\r\n" );
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document.write( "Now we know the value of k and can restore the values of the first three twrms of this AP\r\n" );
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document.write( " = 2*5+1 = 11;\r\n" );
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document.write( " = 5*5-3 = 22;\r\n" );
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document.write( " = 7*5-2 = 33.\r\n" );
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document.write( "Thus, the progression has first term 11 and the common difference d = 22-11 = 11.\r\n" );
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document.write( "At this point, we know everything about this AP and can easily find each of its terms.\r\n" );
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document.write( "In particular, the 17-th term of this AP is  = + d*(n-1) = 11 + 11*(17-1) = 11 + 11*16 = 187. ANSWER\r\n" );
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document.write( "Solved.\r
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document.write( "This solution is your TEMPLATE to solve many other similar problems.\r
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document.write( "In particular, the other part is a TWIN and can be solved by the same way.\r
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document.write( "Literally follow my solution, step by step.\r
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document.write( "You may report me about your progress.\r
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