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 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.

Step2: Identify $a_1$ and $d$

$a_1 = -11$, $d = -5 - (-11) = 6$

Step3: Substitute into formula

$a_n = -11 + (n-1) \times 6$ which rearranges to $a_n = 6(n-1)-11$

Step4: Match with options

This matches option B.

Answer:

B. $a_n = 6(n-1)-11$