Question

An environmental organization started a new online discussion group. The group had 25 members on its first day, and added 20 new members every day after that. Which recursive sequence correctly shows the number of members the environmental organization has after n days?

Answer 1

To define a recursive sequence for the number of members in the environmental organization's online discussion group, we start by identifying the initial conditions and the rule for adding new members.

1. The initial number of members on the first day (day 0) is 25.
2. Each subsequent day, the group adds 20 new members.

We can define the sequence as follows:

Let \( a(n) \) be the number of members after \( n \) days.

- Base case (initial condition):
\[
a(0) = 25
\]

- Recursive rule:
\[
a(n) = a(n-1) + 20 \quad \text{for } n \geq 1
\]

So, the correct recursive sequence to represent the number of members after \( n \) days is:

- \( a(0) = 25 \)
- \( a(n) = a(n-1) + 20 \) for \( n \geq 1 \)