Mackenzie's Pizzeria made 273 pizzas on Saturday, 273 pizzas on Sunday, 273 pizzas on Monday, and 273 pizzas on Tuesday. What kind of sequence is this?

Break Down the Problem

1. Identify the types of sequences based on the pizza production data given for each day.
2. Determine the characteristics of the sequence formed by the number of pizzas made each day.

Relevant Concepts

1. A sequence can be classified as arithmetic, geometric, or neither.
   • An arithmetic sequence has a constant difference between consecutive terms.
   • A geometric sequence has a constant ratio between consecutive terms.

Analysis and Detail

1. The number of pizzas made each day is as follows:

   • Saturday: 273
   • Sunday: 273
   • Monday: 273
   • Tuesday: 273

2. For the sequence $273, 273, 273, 273$:

   • The difference between any two consecutive terms is $273 - 273 = 0$.
   • Thus, the difference is constant.

3. Arithmetic Sequence Test:

   • Because the difference is constant, this sequence can be classified as an arithmetic sequence with a common difference $d = 0$.

4. Geometric Sequence Test:

   • The ratio of consecutive terms is $\frac{273}{273} = 1$, which is also constant.

Verify and Summarize

1. The sequence is both arithmetic (with a common difference of 0) and geometric (with a common ratio of 1).
2. Since all terms are equal, this reinforces that it fits the definition of an arithmetic sequence.

Final Answer

The sequence of pizzas made each day is both an arithmetic sequence (where the common difference is 0) and a geometric sequence (where the common ratio is 1).