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.

Answer 1

To determine the number of daisy seeds, \( d \), that Joslyn plants on the \( n \)th day, we can analyze the sequence provided:

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

We can observe that the number of seeds planted each day corresponds to powers of 2:

• Day 1: \( 2^0 = 1 \)
• Day 2: \( 2^1 = 2 \)
• Day 3: \( 2^2 = 4 \)
• Day 4: \( 2^3 = 8 \)
• Day 5: \( 2^4 = 16 \)
• Day 6: \( 2^5 = 32 \)

From this, we can conclude that on the \( n \)th day, she is planting \( 2^{(n-1)} \) seeds.

Based on this understanding, here are two true statements:

1. The number of seeds Joslyn plants on day \( n \) is equal to \( 2^{(n-1)} \).
2. The sequence represents a geometric progression where each term is twice the previous term.

These statements accurately describe the pattern of seeds planted over the days.