Question

find a formula for the nth term of the arithmetic sequence. first term -2 common difference 8 $a_n = ?n + quad$

Explanation:

Step1: Recall the arithmetic sequence formula

The formula for the \( n \)-th 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. We can also rewrite it in the form \( a_n=dn+(a_1 - d) \) by expanding: \( a_n=a_1+dn - d=dn+(a_1 - d) \).

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

Given that the first term \( a_1=- 2 \) and the common difference \( d = 8 \).

Step3: Substitute into the rewritten formula

We know that in the form \( a_n=dn+(a_1 - d) \), the coefficient of \( n \) is \( d \), so the coefficient of \( n \) is \( 8 \). Then we calculate the constant term: \( a_1 - d=-2-8=-10 \). So the formula \( a_n = 8n-10 \).

Answer:

The coefficient of \( n \) is \( 8 \) and the constant term is \( - 10 \), so \( a_n=\boldsymbol{8}n+\boldsymbol{(-10)} \) (or \( a_n = 8n-10 \)).