The general term of a sequence is given. determine whether the given sequence is arithmetic, geometric, or neither. if the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = 4n - 2

The sequence is given by the rule .

This means that the first, second and third terms of the sequence, , are as follows:



.

.

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".

Arithmetic; common difference d=4.