Britney is picking berries in the berry patch. She picks 307 berries from the first bush, 294 berries from the second bush, 284 berries from the third bush, and 277 berries from the fourth bush. What kind of sequence is this?

Answer 1

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

Here are the numbers of berries picked from each bush:

1. First bush: 307 berries
2. Second bush: 294 berries
3. Third bush: 284 berries
4. Fourth bush: 277 berries

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

• From the first bush to the second bush: \( 307 - 294 = 13 \)
• From the second bush to the third bush: \( 294 - 284 = 10 \)
• From the third bush to the fourth bush: \( 284 - 277 = 7 \)

Now we can observe the differences:

• The difference from the first to the second is 13.
• The difference from the second to the third is 10.
• The difference from the third to the fourth is 7.

These differences (13, 10, 7) are decreasing in a regular manner:

• From 13 to 10: decrease of 3
• From 10 to 7: decrease of 3

This suggests that the sequence is not an arithmetic sequence, but rather a quadratic sequence, since the second differences are constant (all differences decrease by 3).

Thus, the number of berries picked forms a quadratic sequence.