Question

a sequence is given by an=n2-1 nen prove that it is not ap

Answer 1

$\textbf{Given:}$

$a_n=n^2-1$

$\textbf{To prove:}$

$\text{It is not an A.P}$

$\textbf{Solution:}$

$\text{Consider,}$

$a_n=n^2-1$

$\text{For}\;n=1,\;a_1=1^2-1=1-1=0$

$\text{For}\;n=2,\;a_2=2^2-1=4-1=3$

$\text{For}\;n=3,\;a_3=3^2-1=9-1=8$

$a_2-a_1=3-0=3$

$a_3-a_2=8-3=5$

$\implies\,a_2-a_1{\neq}a_3-a_2$

$\textbf{Hence \bf\,a_n is not an A.P}$

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