JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    If \[\left| x \right|,|x-1|\And |x+1|\] are first three terms of an AP, then sum of first 10 terms of sequence is

    A)  25                         

    B)  30     

    C)  40                         

    D)  75

    Correct Answer: A

    Solution :

    As terms are in AP, so \[2|x-1|=|x|+|x+1|\] for\[x\le -1\Rightarrow 2=-1\] (Not possible) for \[-1<x\le 0\Rightarrow x=\frac{1}{2}\] (Not possible) for \[0<x\le 1\Rightarrow x=\frac{1}{4}\] (possible) for \[x>1\Rightarrow -2=1\] (Not possible) \[\therefore \]sequence is\[\frac{1}{4},\frac{3}{4},\frac{5}{4}\] \[\therefore \]\[=\frac{10}{2}\left[ \frac{2}{4}+9\times \left( \frac{3}{4}-\frac{1}{4} \right) \right]=25\]

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