Question

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

Answer 1

The sequence is given by the rule $a_n=4n-2$.

This means that the first, second and third terms of the sequence, $a_1, a_2, a_3$, are as follows:

$a_1=4(1)-2=4-2=2$

$a_2=4(2)-2=8-2=6$.

$a_3=4(3)-2=12-2=10$.

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.