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Question

If x,|x+1|,|x1| are first three terms of an A.P. then the sum of its first 20 terms is

A
180
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B
190
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C
350
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D
360
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Solution

The correct options are
A 180
C 350
​​​​​Given 2|x+1|=x+|x1|

Case (i) x1
2(x+1)=x+x12=1
Which is absurd

Case (ii) 1x<1
2(x+1)=x(x1)
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(x1)
x=32
then |x+1|=12
d=12+32=2
Sum of the first 20 terms 10[3+192]=350

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