Question

Fleur loves to pick flowers. On the first day, she had 9 flowers. On the 2nd, she has 16 flowers. On the third, she has 23 flowers

Write the recursive rule to model how many flowers Fleur has.

Answer 1

To find a recursive rule for the number of flowers Fleur has, let's observe the pattern in the number of flowers she has each day:

- On Day 1, she has 9 flowers.
- On Day 2, she has 16 flowers.
- On Day 3, she has 23 flowers.

Now, let's calculate the differences between the number of flowers from day to day:

- From Day 1 to Day 2: 16 - 9 = 7
- From Day 2 to Day 3: 23 - 16 = 7

The difference between the number of flowers from one day to the next is consistently 7. This indicates that the number of flowers increases by 7 each day.

Thus, we can define the recursive rule as follows:

Let \( a_n \) represent the number of flowers Fleur has on day \( n \).

1. Base Case: \( a_1 = 9 \)
2. Recursive Rule: \( a_n = a_{n-1} + 7 \) for \( n > 1 \)

So, the complete recursive rule is:

\[
\begin{cases}
a_1 = 9 \\
a_n = a_{n-1} + 7 \quad \text{for } n > 1
\end{cases}
\]