The sequence is given by the rule [tex]a_n=4n-2[/tex].
This means that the first, second and third terms of the sequence, [tex]a_1, a_2, a_3[/tex], are as follows:
[tex]a_1=4(1)-2=4-2=2[/tex]
[tex]a_2=4(2)-2=8-2=6[/tex].
[tex]a_3=4(3)-2=12-2=10[/tex].
Now, we can clearly see that 10-6=6-2 = 4. The sequence is arithmetic since the difference between two consecutive terms is the same.
We can also clearly see that the common difference is 4.
Remark: even without computing 2, 6, 10 above, we could see that each term contains one more 4 than the previous term. This is the only thing that changed, while 2 remained "intact".
Answer: Arithmetic; common difference d=4.
