Julie is dividing cherries among some bowls. She put 3 cherries in the first bowl, 12 cherries in the second bowl, 48 cherries in the third bowl, and 192 cherries in the fourth bowl. What kind of sequence is this?

Question

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

Answer 1

To determine the type of sequence Julie is using for the cherries in the bowls, let's take a look at the amounts in each bowl:

• First bowl: 3 cherries
• Second bowl: 12 cherries
• Third bowl: 48 cherries
• Fourth bowl: 192 cherries

Now, let's check if the sequence is arithmetic or geometric.

1. Arithmetic Sequence: This type of sequence has a constant difference between consecutive terms.

   • Difference between 12 and 3 = 12 - 3 = 9
   • Difference between 48 and 12 = 48 - 12 = 36
   • Difference between 192 and 48 = 192 - 48 = 144
   • The differences are not constant.

2. Geometric Sequence: This type of sequence has a constant ratio between consecutive terms.

   • Ratio of the second bowl to the first bowl = 12 / 3 = 4
   • Ratio of the third bowl to the second bowl = 48 / 12 = 4
   • Ratio of the fourth bowl to the third bowl = 192 / 48 = 4
   • The ratios are constant and equal to 4.

Since the sequence has a constant ratio and is not arithmetic, it is classified as:

B) geometric.