To analyze the sequence of the number of daisy seeds Joslyn planted (1, 2, 4, 8, 16, 32), let's identify its properties.
- Pattern of the sequence: This list represents the powers of 2:
- 1 = \( 2^0 \)
- 2 = \( 2^1 \)
- 4 = \( 2^2 \)
- 8 = \( 2^3 \)
- 16 = \( 2^4 \)
- 32 = \( 2^5 \)
From this, we can see that the number of seeds planted on the nth day can be expressed as:
- \( d = 2^{(n-1)} \)
Next, we can evaluate the provided statements:
A. The sequence is arithmetic.
This is false. In an arithmetic sequence, each term is obtained by adding a constant to the previous term. In this case, the differences between successive terms are not constant (1, 2, 4, 8, 16, ...).
B. The sequence is geometric.
This is true. In a geometric sequence, each term is obtained by multiplying the previous term by a constant (in this case, each term is multiplied by 2).
C. The sequence is represented by d = 2n.
This is false. The correct representation for the nth day's planting in terms of power of 2 is \( d = 2^{(n-1)} \), not \( d = 2n \).
D. The sequence is represented by d = 2n-1.
This is false. This expression would imply \( d \) equals \( 2n - 1 \), which does not correctly represent the sequence where \( d = 2^{(n-1)} \).
Based on the evaluations, the two true statements are:
B. The sequence is geometric.
C. The sequence is represented by d=2n.
However, it should be noted that statement C is incorrect based on the observed pattern, and instead the true representation is related to powers of 2.
So only the correct statements from the options given are:
- B. The sequence is geometric.
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