Question

Justify whether it is true to say that $-1,-\frac{3}{2},-2,\frac{5}{2},...$forms an AP as ${\mathrm{a}}_2-{\mathrm{a}}_1={\mathrm{a}}_3-{\mathrm{a}}_2$.

• A. True
• B. False

Answer 1

The correct option is B False

Identify the difference between adjacent term in given sequence

For a sequence to be an Arithmetic Progression common difference of the adjacent terms must be same throughout the series.

We have given

$-1,-\frac{3}{2},-2,\frac{5}{2},...$

The difference between second and first term $=-\frac{3}{2}+1=\frac{-1}{2}...\left(\mathrm{i}\right)$

The difference between third and second term $=-2+\frac{3}{2}=\frac{-1}{2}...\left(\mathrm{ii}\right)$

The difference between fourth and third term $=\frac{5}{2}+2=\frac{9}{2}...\left(\mathrm{iii}\right)$

$\because$In equation $\left(\mathrm{i}\right),\left(\mathrm{ii}\right)$ value of common difference is different that of $\left(\mathrm{iii}\right)$.

$\therefore$The sequence $-1,-\frac{3}{2},-2,\frac{5}{2},...$ is not Arithmetic Progression.

Hence, the given statement is False.