Question:
Justify whether it is true to say that $-1, \frac{-3}{2},-2, \frac{5}{2} \ldots$ forms an AP as $a_{2}-a_{1}=a_{3}-a_{2}$
Solution:
False
Here, $a_{1}=-1, a_{2}=\frac{-3}{2}, a_{3}=-2$ and $a_{4}=\frac{5}{2}$
$a_{2}-a_{1}=\frac{-3}{2}+1=-\frac{1}{2}$
$a_{3}-a_{2}=-2+\frac{3}{2}=-\frac{1}{2}$
$a_{4}-a_{3}=\frac{5}{2}+2=\frac{9}{2}$
Clearly, the difference of successive terms is not same, all though, a2 – a1 = a3 -a2
but a3 – a2 a4 – a3, therefore it does not form an AP.
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