Question

A baker is putting cupcakes on trays to cool. She put 4 cupcakes on the first tray, 12 cupcakes on the second tray, 36 cupcakes on the third tray, and 108 cupcakes on the fourth tray. What kind of sequence is this?

Answer 1

To determine the type of sequence formed by the number of cupcakes on each tray, let's examine the amounts given:

- First tray: 4 cupcakes
- Second tray: 12 cupcakes
- Third tray: 36 cupcakes
- Fourth tray: 108 cupcakes

Now, let's look at the sequence:

1. **First term (a_1):** 4
2. **Second term (a_2):** 12
3. **Third term (a_3):** 36
4. **Fourth term (a_4):** 108

Next, let's identify the ratio of consecutive terms:

- \( \frac{a_2}{a_1} = \frac{12}{4} = 3 \)
- \( \frac{a_3}{a_2} = \frac{36}{12} = 3 \)
- \( \frac{a_4}{a_3} = \frac{108}{36} = 3 \)

Since the ratio between each pair of consecutive terms is constant and equal to 3, this sequence is a **geometric sequence** with a common ratio of 3.

Thus, the sequence of cupcakes on the trays is a **geometric sequence**.