Question

find a formula for the nth term of the arithmetic sequence. first term -17 common difference 5 $a_n = ?n + quad$

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference. Also, we can expand it to \( a_n=dn+(a_1 - d) \).

Step2: Identify \( a_1 \) and \( d \)

Given \( a_1=- 17 \) and \( d = 5 \).

Step3: Substitute into the expanded formula

Substitute \( a_1=-17 \) and \( d = 5 \) into \( a_n=dn+(a_1 - d) \).
First, calculate the coefficient of \( n \), which is \( d = 5 \).
Then, calculate the constant term: \( a_1 - d=-17-5=-22 \).

Answer:

\( a_n = 5n + (-22) \) (or \( a_n = 5n - 22 \))