Question

Define the type of sequence below.

2, 0, 2, 4, 6, ....
O A. neither arithmetic nor geometric
O B. geometric
O C. both arithmetic and geometric
O D. arithmetic

Answer 1

A Because yeah it’s just a

Answer 2

Answer: A. Neither arithmetic nor geometric

========================================================

Step-by-step explanation:

Going from the first term to the second, we add on -2

Then going from the second term to the third, we add on +2

This inconsistency (-2 vs +2) means we don't have a common difference, and therefore the sequence is not arithmetic.

------------

Now let's divide each term by their previous term

term2/term1 = 0/2 = 0

term3/term2 = 2/0 = undefined

We can stop here and conclude that we don't have a common ratio either, so this sequence is not geometric.

------------

Side note: The subsequence 0,2,4,6,... is arithmetic with common difference d = 2 because we add 2 to each term. It's that first 2 in the original sequence that breaks everything.