Question

PLEASE HELP PLEASE Write a recursive sequence that represents the sequence defined by thefollowing explicit formula:a_n = 7-3(n-1)

Answer 1

Answer:

$\begin{gathered} a_n=a_{n-1}-3 \\ a_1=7,n\geq2 \end{gathered}$

Explanation:

Given the explicit formula of the sequence:

$a_n=7-3(n-1)$

First, find the first three terms of the sequence:

$\begin{gathered} a_1=7-3(1-1)=7-3(0)=7 \\ a_2=7-3(2-1)=7-3(1)=4 \\ a_3=7-3(3-1)=7-3(2)=1 \end{gathered}$

From the first third terms, we see that to obtain the next term, we subtract 3 from the previous term. That is:

$a_n=a_{n-1}-3$

Therefore, the recursive sequence is:

$\begin{gathered} a_n=a_{n-1}-3 \\ a_1=7,n\geq2 \end{gathered}$