Question
Which recursive formula can be used to define this sequence for n>1? 2, 4, 8, 16, 32, 64, ...
Answers
Answered by
GPT-4o mini
The given sequence is: 2, 4, 8, 16, 32, 64, ...
This sequence can be observed to be a geometric sequence where each term is twice the previous term. The first term \( a_1 \) is 2.
To define this sequence recursively for \( n > 1 \), we can express the \( n \)-th term in terms of the \((n-1)\)-th term. The recursive formula can be written as:
- \( a_1 = 2 \) (the first term)
- \( a_n = 2 \cdot a_{n-1} \) for \( n > 1 \)
So the recursive formula is:
\[
\begin{align*}
a_1 & = 2 \\
a_n & = 2 \cdot a_{n-1} \quad \text{for } n > 1
\end{align*}
\]
This sequence can be observed to be a geometric sequence where each term is twice the previous term. The first term \( a_1 \) is 2.
To define this sequence recursively for \( n > 1 \), we can express the \( n \)-th term in terms of the \((n-1)\)-th term. The recursive formula can be written as:
- \( a_1 = 2 \) (the first term)
- \( a_n = 2 \cdot a_{n-1} \) for \( n > 1 \)
So the recursive formula is:
\[
\begin{align*}
a_1 & = 2 \\
a_n & = 2 \cdot a_{n-1} \quad \text{for } n > 1
\end{align*}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!