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JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    The solution of the equation\[(x+1)+(x+4)+(x+7)+.........+(x+28)=155\] is 

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: A

    Solution :

    We have \[(x+1)+(x+4)+.........+(x+28)=155\] Let \[n\] be the number of terms in the A.P. on L.H.S. Then \[x+28=(x+1)+(n-1)3\]\[\Rightarrow \]\[n=10\] \[\therefore \] \[(x+1)+(x+4)+......+(x+28)=155\] \[\Rightarrow \] \[\frac{10}{2}[(x+1)+(x+28)]=155\]\[\Rightarrow \]\[x=1\].


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