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Justify whether it is true to say that $-1,-\frac{3}{2},-2, \frac{5}{2}, \ldots$ forms an A.P.as $a_2 - a_1 = a_3 - a_2.$

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Answer. [True]

Solution.

$-1,-\frac{3}{2},-2, \frac{5}{2}, \ldots \ldots \\ \text{here} \ \ \mathrm{a}_{1}=-1 \ \ \mathrm{a}_{2}=-\frac{3}{2} \ \ \mathrm{a}_{3}=-2 \ \ \mathrm{a}_{4}=\frac{5}{2}$
$\\ a_{2}-a_{1}=-\frac{3}{2}-(-1)=\frac{-3}{2}+1=\frac{-3+2}{2}=\frac{-1}{2} \\\\ a_{3}-a_{2}=-2-\left(\frac{-3}{2}\right)=-2+\frac{3}{2}=\frac{-4+3}{2}=\frac{-1}{2}$
$\text{Here}$ $a_{2}-a_{1}=a_{3}-a_{2},$ $\text{Hence it is an A P }$

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