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 represent the number of members in the environmental organization as a recursive sequence, we can define it as follows:

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

1. **Initial condition**: On the first day (when \( n = 0 \)), the number of members is 25. So:
\[
a_0 = 25
\]

2. **Recursive relation**: Each day, the organization adds 20 new members. Thus, for each subsequent day:
\[
a_n = a_{n-1} + 20 \quad \text{for } n \geq 1
\]

Combining these two parts, the recursive sequence that shows the number of members after \( n \) days is:

\[
\begin{align*}
a_0 &= 25, \\
a_n &= a_{n-1} + 20 \quad \text{for } n \geq 1.
\end{align*}
\]