Answer:- The sequence is arithmetic because the terms have a common difference.
Explanation:-
From the given graph , it can be seen that
At n=2, [tex]a_2=9[/tex]
at n=3 , [tex]a_3=7.5[/tex]
at n=4 , [tex]a_n=6[/tex]
at n=5 , [tex]a_n=4.5[/tex]
And we know that in arithmetic progression
[tex]a_{n+1}=a_n+d \text{ , where n is the number of terms and d is the common difference }\\\Rightarrow\ a_3=a_2+d\\\Rightarrow\ d=a_3-a_2=7.5-9=-1.5[/tex]
[tex]a_4=a_3+d\\\Rightarrow\ d=a_4-a_3=6-7.5=-1.5\\a_5=a_4+d\\\Rightarrow\ d=a_5-a_6=4.5-6=-1.5[/tex]
Similarly we can see the common difference is same for all consecutive values of n .
Thus the sequence showed by the graph is arithmetic because the terms have a common difference.
