Emmy is picking berries in the berry patch. She picks 187 berries from the first bush, 169 berries from the second bush, 151 berries from the third bush, and 133 berries from the fourth bush. What kind of sequence is this?

Question

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

Answer 1

To determine the type of sequence formed by the number of berries picked from each bush, we can look at the differences between the number of berries picked.

Here are the numbers:

• First bush: 187
• Second bush: 169
• Third bush: 151
• Fourth bush: 133

Now, let's calculate the differences between consecutive bushes:

1. From the first bush (187) to the second bush (169): \[ 187 - 169 = 18 \]

2. From the second bush (169) to the third bush (151): \[ 169 - 151 = 18 \]

3. From the third bush (151) to the fourth bush (133): \[ 151 - 133 = 18 \]

The differences between each pair of consecutive terms are consistently 18, indicating that this sequence is arithmetic.

A geometric sequence involves each term being multiplied by a constant factor to get to the next term, which is not observed here.

Therefore, the sequence is arithmetic.

The correct answer is: A) arithmetic