1.

Justify whether it is true to say that ` -1, (-3)/(2), -2, (5)/(2), … ` Forms an AP as `a_(2)-a_(1)=a_(3)-a_(2)`.

Answer» False
Here, `a_(1)= -1, a_(2)=(-3)/(2), a_(3)= -2` and `a_(4)= (5)/(2)`
`a_(2)-a_(1)= (-3)/(2)+1=-(1)/(2)`
`a_(3)-a_(2)= -2+(3)/(2)= -(1)/(2)`
`a_(4)-a_(3)=(5)/(2)+2=(9)/(2)`
Clearly, the difference of successive terms is not same, all though, `a_(2)-a_(1)=a_(3)-a_(2)` but `a_(3)-a_(2) ne a_(4)-a_(3)` therefore it does not form an AP.


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