Algebra.Com's Answer #852200 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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Tim did 10 lunges on day 1 and continued this doing 4 more lunges on each day.
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document.write( "On day 7th he took a break and did not do any day.
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document.write( "What is the equation for this?
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document.write( "express it in the form y=ax(x+b)+c, where a, b and c are constants. x= no of days and y=no of lunges Tim Did
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document.write( "The numbers of lunges per day form arithmetic progression with the first term of  = 10\r\n" );
document.write( "and the common difference of d = 4.\r\n" );
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document.write( "Use the formula for the sum of first n terms of an arithmetic progression\r\n" );
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document.write( "  =  . (1)\r\n" );
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document.write( "In your problem\r\n" );
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document.write( " =  .\r\n" );
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document.write( "They want you use x instead of n and y instead of .\r\n" );
document.write( "OK. Then the formula takes the form\r\n" );
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document.write( " y =  = 2(x-1)*x + 10x = 2x^2 - 2x + 10x = 2x^2 + 8x = 2x(x+4).\r\n" );
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document.write( "Thus, your final formula is\r\n" );
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document.write( " y = 2x*(x+4), 1 <= x <= 6. (2)\r\n" );
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document.write( "Comparing with the form y = ax(x+b) + c, you see for the coefficients 'a', 'b' and 'c'\r\n" );
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document.write( " a = 2; b = 4; c = 0. (3)\r\n" );
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document.write( "Below in the Table, calculations are compared using formulas (2), (3) with direct calculations of the cumulative sum \r\n" );
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document.write( " T A B L E \r\n" );
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document.write( "day every cumulative sum cumulative sum\r\n" );
document.write( " day computed directly computed by formula (2)\r\n" );
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document.write( " 1 10 10 10\r\n" );
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document.write( " 2 14 24 24\r\n" );
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document.write( " 3 18 42 42\r\n" );
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document.write( " 4 22 64 64\r\n" );
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document.write( " 5 26 90 90\r\n" );
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document.write( " 6 30 120 120\r\n" );
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document.write( "ANSWER. For the given sequence, the formula is y = 2x*(x+4).\r\n" );
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document.write( "Solved.\r
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