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} . $

AcademicMathematicsNCERTClass 10

Given:

Given sequence is \( -1,-\frac{3}{2},-2, \frac{5}{2}, \ldots \)

To do:

We have to check 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:

In the given sequence,

$a_1=-1, a_2=-\frac{3}{2}, a_3=-2, a_4=\frac{5}{2}$

$a_2-a_1=-\frac{3}{2}-(-1)=-\frac{3}{2}+1=\frac{-3+2}{2}=\frac{-1}{2}$

$a_3-a_2=-2-(-\frac{3}{2})=--2+\frac{3}{2}=\frac{-4+3}{2}=\frac{-1}{2}$

$a_4-a_3=\frac{5}{2}-(-2)=\frac{5}{2}+2=\frac{5+4}{2}=\frac{9}{2}$

Here,

$a_2 - a_1 = a_3 - a_2$ but $a_4 - a_3≠a_3 - a_2$

Therefore, the given sequence is not an AP. 

raja
Updated on 10-Oct-2022 13:27:27

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