Question

Show that the sequence defined by an=5n-7 is an A.P., find its common difference.

Answer 1

$\textbf{Given:}$

$a_n=5n-7$

$\text{For n=1,}\;a_1=5-7=-2$

$\text{For n=2,}\;a_2=10-7=3$

$\text{For n=3,}\;a_3=15-7=8$

$\text{For n=4,}\;a_1=20-7=13$

$\implies\,a_2-a_1=a_3-a_2=a_4-a_3=........=5$

$\therefore$The sequence defined by $\;a_n\;\;$ is an A.P

$\textbf{Also, Common difference is 5}$

Find more:

In an A.P. if Sn = 3n2 - n and its common difference is ‘6’ then first term is ______

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