Jackson went out to his garden and cut 5 roses from the first rose bush, 10 roses from the second rose bush, 20 roses from the third rose bush, and 40 roses from the fourth rose bush. What kind of sequence is this?

Question

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

Answer 1

To determine what kind of sequence the number of roses cut from each bush represents, we can analyze the numbers: 5, 10, 20, and 40.

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences:
   • 10 - 5 = 5
   • 20 - 10 = 10
   • 40 - 20 = 20

The differences (5, 10, 20) are not constant, so it is not an arithmetic sequence.

2. Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant. Let's calculate the ratios:
   • 10 / 5 = 2
   • 20 / 10 = 2
   • 40 / 20 = 2

The ratios (2, 2, 2) are constant, indicating that this is a geometric sequence.

Since the sequence is geometric but not arithmetic, the answer is:

B) geometric.