Perry buys a bag of 20 carrots on the first day. The second day, he eats half of the bag. Each day after, he eats half of what is left in the bag. Create a sequence formula that describes the number of carrots Perry will have on any given day.

Question

use two of these:
(1/2)^n-1, 2, 20, (1/20)^n-1

Answer 1

To describe the number of carrots Perry has on any given day, we can create a sequence based on the information given.

Let's denote the number of carrots Perry has on day \( n \) as \( C(n) \):

• On the first day (\( n = 1 \)), he starts with 20 carrots: \[ C(1) = 20 \]

• On the second day (\( n = 2 \)), he eats half of the 20 carrots he had: \[ C(2) = 20 - \frac{20}{2} = 20 \times (1 - \frac{1}{2}) = 20 \times \frac{1}{2} = 10 \]

• On the third day (\( n = 3 \)), he eats half of what is left: \[ C(3) = 10 \times \frac{1}{2} = 10 \times (1 - \frac{1}{2}) = 10 \]

• Continuing this pattern, on day \( n \): \[ C(n) = C(n-1) \times \frac{1}{2} \]

The general formula for the number of carrots remaining can be formulated as: \[ C(n) = 20 \times \left( \frac{1}{2} \right)^{n-1} \]

Thus, the sequence formula that describes the number of carrots Perry will have on any given day \( n \) is: \[ C(n) = 20 \times \left( \frac{1}{2} \right)^{n-1} \]

This formula incorporates the first two of the options you provided, specifically \( 20 \) and \( (1/2)^{n-1} \).