oslyn is planting daisy seeds in a flower garden. Each day, she plants a different number of seeds. The list below shows the number of seeds Joslyn planted on each of the first six days.

1, 2, 4, 8, 16, 32

Joslyn wants to determine the number of daisy seeds, d, she should plant on the nth day. Which statements below are true? Select two that apply.

A.
The sequence is arithmetic.

B.
The sequence is geometric.

C.
The sequence is represented by d = 2n.
D.
The sequence is represented by d = 2n - 1.

E.
The sequence is represented by d = 2^n.

F.
The sequence is represented by d = 2^n - 1.

1 answer

To analyze the sequence of daisy seeds planted by Joslyn, we can look at the values given: 1, 2, 4, 8, 16, 32.

  1. Arithmetic Sequence: An arithmetic sequence has a common difference between consecutive terms. Here, the differences are 1, 2, 4, 8, and 16, which are not constant. Therefore, statement A is false.

  2. Geometric Sequence: A geometric sequence has a common ratio between consecutive terms. The ratios here are 2, 2, 2, 2, and 2, which are constant. Therefore, statement B is true.

  3. Formula d = 2n: This formula means that on day n, the number of seeds planted would be 2 times n. For example, on day 1, it would be 2 (which is incorrect as she planted 1). Therefore, statement C is false.

  4. Formula d = 2n - 1: This suggests that the first day's planting (n=1) would be 1, the second day (n=2) would be 3, and so on. The values do not match with the provided sequence. Therefore, statement D is false.

  5. Formula d = 2^n: Here, on the first day (n=1), the value would be 2^1 = 2 (which does not match the sequence). Therefore, statement E is false.

  6. Formula d = 2^n - 1: This suggests that on day 1 (n=1), d = 2^1 - 1 = 1, on day 2 (n=2), d = 2^2 - 1 = 3, and so on. This does not correspond to the values given either. Therefore, statement F is also false.

After analyzing each statement, the only true statement about Joslyn's planting of daisies is option:

  • B: The sequence is geometric.
  • E: The sequence is represented by d = 2^n (if we consider that it can also be represented starting at n=0).

So, the correct answers based on the provided information are B and E.