Question

the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$? a $a_n = -11(n - 1) - 6$ b $a_n = 6(n - 1) - 11$ c $a_n = -11(n - 1) + 6$ d $a_n = -6(n - 1) - 11$

Explanation:

Step1: Recall 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.

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

From the sequence \(-11,-5,1,7\), the first term \(a_1=-11\). The common difference \(d\) is calculated as \(-5-(-11)=6\), \(1 - (-5)=6\), \(7 - 1 = 6\), so \(d = 6\).

Step3: Substitute into the formula

Substitute \(a_1=-11\) and \(d = 6\) into \(a_n=a_1+(n - 1)d\), we get \(a_n=-11+(n - 1)\times6\), which can be rewritten as \(a_n=6(n - 1)-11\).

Answer:

B. \(a_{n}=6(n - 1)-11\)