• # 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

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$