Question
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.
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, 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
Answers
GPT-4o mini
To analyze the sequence of seeds Joslyn planted each day, let's look at the numbers she planted:
1 (Day 1),
2 (Day 2),
4 (Day 3),
8 (Day 4),
16 (Day 5),
32 (Day 6)
Now let's evaluate the potential true statements:
A. The sequence is arithmetic.
- This statement is **false** because in an arithmetic sequence, the difference between consecutive terms is constant. Here, the differences are not constant (1, 2, 4, 8, 16).
B. The sequence is geometric.
- This statement is **true** because in a geometric sequence, each term after the first is found by multiplying the previous term by a constant factor. In this case, each term is multiplied by 2 (1 × 2 = 2, 2 × 2 = 4, etc.).
C. The sequence is represented by d = 2n.
- This statement is **false** for the given days because if we consider n = 1, we have d = 2^1 = 2, which does not match the first term of 1.
D. The sequence is represented by d = 2n-1.
- This statement is **false** since substituting n=1 gives d = 2^(1) - 1 = 1, which is correct for the first day, but does not work for the remaining days.
E. The sequence is represented by d = 2^n.
- This statement is **false** under the assumption n starts at 1. If we use d = 2^n, then for n=1, d should be 2^1 = 2.
F. The sequence is represented by d = 2^n - 1.
- This statement is **true** for the first day. If we use d = 2^n - 1, for n=1, d = 2^1 - 1 = 1. This matches the first term.
So the two statements that are correct are:
**B. The sequence is geometric.**
**F. The sequence is represented by d = 2^n - 1.**
1 (Day 1),
2 (Day 2),
4 (Day 3),
8 (Day 4),
16 (Day 5),
32 (Day 6)
Now let's evaluate the potential true statements:
A. The sequence is arithmetic.
- This statement is **false** because in an arithmetic sequence, the difference between consecutive terms is constant. Here, the differences are not constant (1, 2, 4, 8, 16).
B. The sequence is geometric.
- This statement is **true** because in a geometric sequence, each term after the first is found by multiplying the previous term by a constant factor. In this case, each term is multiplied by 2 (1 × 2 = 2, 2 × 2 = 4, etc.).
C. The sequence is represented by d = 2n.
- This statement is **false** for the given days because if we consider n = 1, we have d = 2^1 = 2, which does not match the first term of 1.
D. The sequence is represented by d = 2n-1.
- This statement is **false** since substituting n=1 gives d = 2^(1) - 1 = 1, which is correct for the first day, but does not work for the remaining days.
E. The sequence is represented by d = 2^n.
- This statement is **false** under the assumption n starts at 1. If we use d = 2^n, then for n=1, d should be 2^1 = 2.
F. The sequence is represented by d = 2^n - 1.
- This statement is **true** for the first day. If we use d = 2^n - 1, for n=1, d = 2^1 - 1 = 1. This matches the first term.
So the two statements that are correct are:
**B. The sequence is geometric.**
**F. The sequence is represented by d = 2^n - 1.**