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
.
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
.
Answers
GPT-4o mini
To analyze the sequence of seeds Joslyn planted, we see the numbers are: 1, 2, 4, 8, 16, 32.
1. The sequence is not arithmetic because the difference between consecutive terms isn't constant (e.g., 2 - 1 = 1, 4 - 2 = 2, 8 - 4 = 4, etc.).
2. The sequence is geometric because each term is multiplied by 2 to get the next term (1 * 2 = 2, 2 * 2 = 4, etc.). This gives the common ratio of 2.
3. The terms can be represented by \( d = 2^n \), where \( n \) is the index of the day (starting from 0). For instance, on day 0 (1st day), \( d = 2^0 = 1\); on day 1 (2nd day), \( d = 2^1 = 2\); on day 2 (3rd day), \( d = 2^2 = 4\) and so on.
Thus, the correct answers are:
**B. The sequence is geometric.**
**E. The sequence is represented by \( d = 2^n \).**
1. The sequence is not arithmetic because the difference between consecutive terms isn't constant (e.g., 2 - 1 = 1, 4 - 2 = 2, 8 - 4 = 4, etc.).
2. The sequence is geometric because each term is multiplied by 2 to get the next term (1 * 2 = 2, 2 * 2 = 4, etc.). This gives the common ratio of 2.
3. The terms can be represented by \( d = 2^n \), where \( n \) is the index of the day (starting from 0). For instance, on day 0 (1st day), \( d = 2^0 = 1\); on day 1 (2nd day), \( d = 2^1 = 2\); on day 2 (3rd day), \( d = 2^2 = 4\) and so on.
Thus, the correct answers are:
**B. The sequence is geometric.**
**E. The sequence is represented by \( d = 2^n \).**