Question

find a formula for the nth term of the arithmetic sequence. first term 9 common difference -2 $a_n = ?n + $

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 \( a_1 = 9 \) (first term) and \( d=- 2 \) (common difference).

Step3: Find the coefficient of \( n \) and the constant term

In the form \( a_n=dn + c \) (where \( c=a_1 - d \)):

• The coefficient of \( n \) is \( d=-2 \).
• The constant term \( c=a_1 - d=9-(-2)=9 + 2 = 11\).

So the formula for the \( n \)-th term is \( a_n=-2n + 11 \).

Answer:

\( a_n=-2n + 11 \) (So the first box is \(-2\) and the second box is \(11\))