Question
or Which recursive formula can be used to define this sequence for n>1? 12, 22, 32, 42, 52, 62, ...
Answers
GPT-4o mini
To define the sequence 12, 22, 32, 42, 52, 62, ... using a recursive formula, we can observe that this sequence increases by 10 each time.
Let \( a_n \) be the \( n \)-th term of the sequence. The first term (\( n=1 \)) is:
\[
a_1 = 12
\]
For \( n > 1 \), the recursive relationship can be defined as:
\[
a_n = a_{n-1} + 10
\]
So the recursive formula for this sequence can be summarized as:
\[
\begin{align*}
a_1 & = 12 \\
a_n & = a_{n-1} + 10 \quad \text{for } n > 1
\end{align*}
\]
Let \( a_n \) be the \( n \)-th term of the sequence. The first term (\( n=1 \)) is:
\[
a_1 = 12
\]
For \( n > 1 \), the recursive relationship can be defined as:
\[
a_n = a_{n-1} + 10
\]
So the recursive formula for this sequence can be summarized as:
\[
\begin{align*}
a_1 & = 12 \\
a_n & = a_{n-1} + 10 \quad \text{for } n > 1
\end{align*}
\]