Joslyn 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.

Question

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.

Answer 1

To determine which statements are true regarding the number of daisy seeds Joslyn planted, let's analyze the sequence provided: 1, 2, 4, 8, 16, 32.

1. Identify the nature of the sequence:

   • The numbers in the list are:
     • Day 1: 1 (2^0)
     • Day 2: 2 (2^1)
     • Day 3: 4 (2^2)
     • Day 4: 8 (2^3)
     • Day 5: 16 (2^4)
     • Day 6: 32 (2^5)

   This clearly indicates that the number of seeds is doubling each day, which is characteristic of a geometric sequence.

2. Checking the options:

   • A. The sequence is arithmetic.

     • False. An arithmetic sequence has a constant difference between consecutive terms. Here, the ratio between consecutive terms is constant, but the difference is not.

   • B. The sequence is geometric.

     • True. Each term is obtained by multiplying the previous term by 2. The ratio between consecutive terms is constant (2), which defines a geometric sequence.

   • C. The sequence is represented by d=2n.

     • False. This would give:
       • Day 1: 2^1 = 2
       • Day 2: 2^2 = 4
       • Day 3: 2^3 = 8, etc. This does not match the sequence.

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

     • False. This would yield:
       • Day 1: 2^0 = 1
       • Day 2: 2^1 = 2
       • Day 3: 2^2 = 4, etc. This matches, but it is more correctly represented by the related power of 2 function.

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

     • False. This expression would produce:
       • Day 1: 2^1 = 2
       • Day 2: 2^2 = 4, etc., which is incorrect.

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

     • True. This would yield:
       • Day 1: 2^1 - 1 = 1
       • Day 2: 2^2 - 1 = 3
       • Day 3: 2^3 - 1 = 7, which is not the original sequence. Thus this option is false.

Therefore, the two true statements are:

• B. The sequence is geometric.
• (No second true statement from the choices given)

The correct functions to represent the given sequence of seeds on respective days is d = 2^(n-1) which is not listed in the provided answers. The only truly representative statement about the nature of the sequence from the provided options is statement B.

Answer 2

are you sure

Answer 3

Let’s clarify the analysis step by step for Joslyn’s planting of daisy seeds.

The sequence of seeds planted over the first six days is:

• Day 1: 1 seed
• Day 2: 2 seeds
• Day 3: 4 seeds
• Day 4: 8 seeds
• Day 5: 16 seeds
• Day 6: 32 seeds

From this, we can observe:

1. Type of Sequence:

   • The numbers being planted are 1, 2, 4, 8, 16, 32, which are powers of 2.
   • Day 1 corresponds to \(2^0\) (1), Day 2 corresponds to \(2^1\) (2), Day 3 corresponds to \(2^2\) (4), Day 4 corresponds to \(2^3\) (8), Day 5 corresponds to \(2^4\) (16), and Day 6 corresponds to \(2^5\) (32).

   This means the number of seeds planted on the nth day is generally described by \(d = 2^{n-1}\).

2. Evaluating the Options:

   • A. The sequence is arithmetic.

     • False. The difference between terms is not constant; it doubles each day.

   • B. The sequence is geometric.

     • True. Each term is obtained by multiplying the previous term by 2, which defines a geometric sequence with a common ratio of 2.

   • C. The sequence is represented by \(d=2n\).

     • False. This gives 2 seeds on Day 1, which is incorrect.

   • D. The sequence is represented by \(d=2^{n-1}\).

     • True. This correctly represents the sequence since Day 1 would be \(2^0 = 1\), Day 2 would be \(2^1 = 2\), and so on.

   • E. The sequence is represented by \(d=2^n\).

     • False. This gives Day 1 as 2, which is incorrect.

   • F. The sequence is represented by \(d=2^n - 1\).

     • False. This gives Day 1 as \(2^1 - 1 = 1\), Day 2 as \(2^2 - 1 = 3\), which does not maintain the same sequence.

Final Correct Statements:

• B. The sequence is geometric.
• D. The sequence is represented by \(d = 2^{n-1}\) (but this option was not explicitly listed, only if interpreted).

Therefore, the correct statements from your provided options based on this analysis are:

• B. The sequence is geometric.
• D. The sequence is represented by \(d=2^{n-1}\) (if we consider the common adjustment).

Apologies for the confusion in my prior response regarding the representation. There is no explicit correct choice for the exact formula I identified, but B is indeed true.