Question

Which of the following is true about the sequence graphed below?

The sequence is arithmetic because the terms have a common difference.The sequence is arithmetic because the terms do not have a common difference.The sequence is not arithmetic because the terms have a common difference. The sequence is not arithmetic because the terms do not have a common difference.

Answer 1

The sequence is arithmetic because the terms have a common difference.

Explanation:

A on edg 2022

Answer 2

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,
`a_2=9`

at n=3 ,
`a_3=7.5`

at n=4 ,
`a_n=6`

at n=5 ,
`a_n=4.5`

And we know that in arithmetic progression

`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`

`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`

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.