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Question

# If x,|x+1|,|x−1| are first three terms of an A.P., then the maximum possible sum of the first 20 terms is

A
350
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B
180
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C
370
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D
x,|x+1|,|x1| cannot be first three terms of an A.P. for all xR
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Solution

## The correct option is A 350​​​​​Given 2|x+1|=x+|x−1| Case (i) x≥1 2(x+1)=x+x−1⇒2=−1 Which is absurd Case (ii) −1≤x<1 2(x+1)=x−(x−1) ⇒x=−12 then |x+1|=12 ⇒d=12+12=1 Sum of first 20 terms =10[−1+19]=180 Case (iii) x<−1 −2(x+1)=x−(x−1) ⇒x=−32 then |x+1|=12 ⇒d=12+32=2 Sum of the first 20 terms 10[−3+19⋅2]=350

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