Question

find a formula for the nth term of the arithmetic sequence. first term 11 common difference 5 $a_n = ?n + \square$ hint: the coefficient of n is the common difference.

Explanation:

Step1: Recall arithmetic sequence formula

The general 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 \(d\) and \(a_1\)

Given that the first term \(a_1 = 11\) and the common difference \(d=5\).

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

From the form \(a_n=dn+(a_1 - d)\), the coefficient of \(n\) is the common difference \(d\), so the coefficient of \(n\) is \(5\). Then the constant term is \(a_1 - d=11 - 5 = 6\). So the formula is \(a_n = 5n+6\).

Answer:

The coefficient of \(n\) is \(5\) and the constant term is \(6\), so \(a_n=\boldsymbol{5}n+\boldsymbol{6}\)