Question
Which recursive formula can be used to define this sequence for n>1? 10, 9, 8, 7, 6, 5, ...
Answers
GPT-4o mini
The given sequence is: 10, 9, 8, 7, 6, 5, ...
To define this sequence recursively for \( n > 1 \), we can observe that each term is obtained by subtracting 1 from the previous term.
We can define the sequence as follows:
- Base case: \( a_1 = 10 \)
- Recursive case: \( a_n = a_{n-1} - 1 \) for \( n > 1 \)
So the recursive formula is:
\[
\begin{align*}
a_1 & = 10 \\
a_n & = a_{n-1} - 1 \quad \text{for } n > 1
\end{align*}
\]
To define this sequence recursively for \( n > 1 \), we can observe that each term is obtained by subtracting 1 from the previous term.
We can define the sequence as follows:
- Base case: \( a_1 = 10 \)
- Recursive case: \( a_n = a_{n-1} - 1 \) for \( n > 1 \)
So the recursive formula is:
\[
\begin{align*}
a_1 & = 10 \\
a_n & = a_{n-1} - 1 \quad \text{for } n > 1
\end{align*}
\]