Celine is stacking cups; she put 21 plastic cups in the first stack, 32 plastic cups in the second stack, 43 plastic cups in the third stack, and 54 plastic cups in the fourth stack. What kind of sequence is this?

Question

A) arithmetic
B) geometric
C) both
D) neither

Answer 1

To determine what kind of sequence Celine's stacks of cups represent, we can analyze the differences between the number of cups in consecutive stacks.

1. The first stack has 21 cups.
2. The second stack has 32 cups. The difference from the first stack is \(32 - 21 = 11\).
3. The third stack has 43 cups. The difference from the second stack is \(43 - 32 = 11\).
4. The fourth stack has 54 cups. The difference from the third stack is \(54 - 43 = 11\).

The differences between consecutive terms are all constant:

• \(32 - 21 = 11\)
• \(43 - 32 = 11\)
• \(54 - 43 = 11\)

Since the differences between consecutive terms are the same, this indicates that the sequence is arithmetic.

In an arithmetic sequence, the common difference between consecutive terms is constant.

Thus, the answer is: A) arithmetic