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?

Question

A.

Answer 1

To create a recursive sequence that models the number of members in the environmental organization after \( n \) days, we need to establish the initial condition and a formula that reflects the growth of members each day.

1. Initial Condition: On day \( n = 0\) (the first day), the number of members is 25.
2. Recursive Formula: Each day after the first, the organization adds 20 new members.

We can define the recursive sequence as follows:

• Let \( a_n \) be the number of members after \( n \) days.
• The initial condition is \( a_0 = 25 \).
• The recursive formula is \( a_n = a_{n-1} + 20 \) for \( n \geq 1 \).

So the recursive sequence is defined as:

\[ \begin{align*} a_0 & = 25 \ a_n & = a_{n-1} + 20 \quad (n \geq 1) \end{align*} \]

This correctly captures the number of members after \( n \) days.