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Math Help - Aritmetic progression in algebra

  1. #1
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    Aritmetic progression in algebra

    f(x)+ 2x, where x is an integer. If we arrange the values f(x) for x= 25,24,23,.....(continuously decreasing value of x), we get an arithmetic progression whose first term is 50. Find the maximum value of the sum of all the terms of A.P.
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  2. #2
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    Quote Originally Posted by jashansinghal View Post
    f(x)+ 2x, where x is an integer. If we arrange the values f(x) for x= 25,24,23,.....(continuously decreasing value of x), we get an arithmetic progression whose first term is 50. Find the maximum value of the sum of all the terms of A.P.
    i think you mean f(x)=2x

    Identify all values of x which makes f(x) positive , ie 25 ,... ,1 since f(0)=0 and f(-1)=-2 ,f(x) will be -ve since then.

    f(25)=50 , f(1)=2

    This AP has first term 50 and last term 2 with common difference -2 ,evaluate the sum then
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  3. #3
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    Actually. This question was given in a book. I copied it as it is. The correct answer is 650.
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  4. #4
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    Quote Originally Posted by jashansinghal View Post
    Actually. This question was given in a book. I copied it as it is. The correct answer is 650.
    Yes, you will get that answer if you follow my steps. Have you tried?
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