Is the sequence $a_{n}=5+9 n$ arithmetic?
Your answer is (input yes or no):
If your answer is yes, its first term is and its common difference is
Answer
\(\boxed{\text{Yes, the sequence } a_{n}=5+9 n \text{ is arithmetic. Its first term is } 5 \text{ and its common difference is } 9.}\)
Step 1 ：Consider the sequence \(a_{n}=5+9 n\).
Step 2 ：We want to determine if this sequence is arithmetic.
Step 3 ：A sequence is arithmetic if it can be written in the form \(a_{n}=a+dn\), where \(a\) is the first term and \(d\) is the common difference.
Step 4 ：Here, we can see that the sequence \(a_{n}=5+9 n\) fits this form, with \(a=5\) and \(d=9\).
Step 5 ：Let's generate the first 10 terms of the sequence to confirm this: [5, 14, 23, 32, 41, 50, 59, 68, 77, 86].
Step 6 ：Indeed, each term is 9 greater than the previous term, confirming that the sequence is arithmetic.
Step 7 ：\(\boxed{\text{Yes, the sequence } a_{n}=5+9 n \text{ is arithmetic. Its first term is } 5 \text{ and its common difference is } 9.}\)
